They refuse to pray in congregation on the grounds that the imam charges a fee for leading the prayers!

Offering prayer in congregation is a duty that is
obligatory upon men who are able to do it, and no one stays away from it
without an excuse except one who is a sinner and has deviated from the
path of guidance. 

Muslim (654) narrated that Ibn Mas‘ood (may Allah be pleased
with him) said: Whoever would like to meet Allah, may He be exalted,
tomorrow as a Muslim, let him regularly offer these prayers where the call
to prayer is given, for Allah has prescribed the Sunnahs of guidance to your
Prophet (blessings and peace of Allah be upon him) and they (the prayers)
are among the Sunnahs of guidance. If you pray in your houses like this one
who stays away from the mosque prays in his house, you will have forsaken
the Sunnah of your Prophet, and if you forsake the Sunnah of your Prophet
you will go astray. There is no man who purifies himself and purifies
himself well, then he goes to one of these mosques, but Allah will record
one good deed for him for every step he takes, and will raise him in status
one degree thereby, and will erase one bad deed thereby. I remember when no
one would stay away from it but a hypocrite whose hypocrisy was known, and a
man would come staggering between two others in order to stand in the row. 

It was narrated that Abu Hurayrah (may Allah be pleased with
him) said: A blind man came to the Prophet (blessings and peace of Allah be
upon him) and said: O Messenger of Allah, I do not have any guide to take me
to the mosque. And he asked the Messenger of Allah (blessings and peace of
Allah be upon him) to grant him a concession allowing him to pray in his
house, and he allowed him that. When he turned to leave, he called him back
and said: “Can you hear the call to prayer?” He said: Yes. He said: “Then
answer it.” 

This hadith was also narrated by Abu Dawood (552), as
follows: “I cannot find any concession for you. 

Ibn al-Mundhir said: 

If there is no concession for a blind man, then it is more
appropriate that there should be no concession for one who is sighted. End
quote. 

Al-Awsat
(4/134). See also: al-Mughni (2/3). 

For more information on the evidence for it being obligatory
to offer prayer in congregation, please see the answer to question no.
8918 

Secondly: 

If the imam receives a salary from the government, whether it
is paid for by the bayt al-maal (treasury) or a waqf to which he is
entitled, or otherwise, there is nothing wrong with that. 

Al-Bahooti said in al-Kashshaaf (1/475): 

If something is given to the imam without any conditions
being stipulated, there is nothing wrong with that according to the texts.
The same applies if that is given to him from the bayt al-maal or from a
waqf. End quote. 

Shaykh al-Fawzaan was asked:

I am an employee in waqf administration, and my job is to
lead religious rituals, in the sense that I act as an imam and receive a
salary for that. Is that permissible? Please note that I have no other
source of income. 

The shaykh (may Allah preserve him) replied: 

There is nothing wrong with you acting as an imam and
receiving what has been allocated for imams from the bayt al-maal of
financial help, because this is helping you to obey Allah. 

This applies so long as your aim is not to seek worldly gain;
rather your aim is to seek that which is with Allah, may He be glorified and
exalted, and your acting as an imam is based on a desire for good, and you
are taking this salary in order to meet your needs so that your time will be
free to act as an imam. There is nothing wrong with this; rather it comes
under the heading of helping people to obey Allah, may He be glorified and
exalted, and what matters is the aims. 

But if a person’s aim is worldly gain, and he is using
worship and acts of obedience as a means of attaining worldly gains, then
this is not permissible, and this is an invalid deed. End quote. 

Al-Muntaqa min Fataawa al-Fawzaan
(49/49-50) 

But if what the imam is paid comes from people’s donations,
there is also nothing wrong with that, if he has not made any stipulations
in that regard; rather whatever they give him he accepts, whether it is
small or great. 

Abu Dawood said: I heard Ahmad (may Allah have mercy on him)
when he was asked about an imam who said: I will lead you in prayer in
Ramadan in return for such and such of money. He said: I ask Allah to keep
us safe and sound; who would pray behind such a man? And it was narrated
from him that he said: Do not pray behind one who does not give zakaah. And
he said: Do not pray behind one who stipulates payment, but there is nothing
wrong with them giving the money without stipulating anything.

End quote from al-Mughni (2/9). 

Ibn Nujaym (may Allah have mercy on him) said: 

They said: If he has not stipulated that they should give him
anything, but they know that he is in need, so they collect something for
him every time, that is good and it is halaal for him. 

End quote from al-Bahr ar-Raa’iq (1/268) 

Thirdly: 

From the above it is clear that simply taking a salary from
the government, or accepting gifts and payment for acting as an imam is not
something for which an imam should be criticised or blamed, because perhaps
he is taking it in an Islamically acceptable manner in which there is
nothing objectionable. In fact some scholars are of the view that it is
permissible for him to receive a salary in all cases, even if the imam is
not poor, and even if he stipulates that they should do that. This is a
reasonable view among some Maaliki, Shaafa‘i and Hanbali fuqaha’. 

See: Akhdh al-Maal ‘ala A‘maal al-Qurab by ‘Aadil
Shaaheen (1/206-220) 

If that is the case, then with regard to such matters, which
are subject to ijtihaad, the one who holds a different view should not be
rebuked, if this is what he believes and thinks most likely to be correct.
So it is more appropriate to say that he should not be criticised or blamed
for that. 

Fourthly: 

Finding out about the imam’s aim in acting as an imam, and
determining that he has no goal except acquiring money, is not something
that people are usually able to do; rather that matter should be left to
Allah, and the imam should be treated according to what appears to be the
case. 

The Messenger of Allah (blessings and peace of Allah be upon
him) said: 

“I have not been instructed to examine people’s hearts or
open their chests (to find out what their real intentions are).” Agreed
upon. 

If it so happens that we find out about that, and come to
know that he is sinning because of that intention, the mere fact that the
imam has committed a sin does not give us an excuse to refrain from playing
in congregation. Rather, whenever it is possible to pray in congregation
behind an imam who is better than him and more religiously committed, that
should be done, but if it is not possible, it is not permissible for anyone
to refrain from praying in congregation just for this reason. This is one of
the basic teachings of the Sunnah. Otherwise, if people were to stop
attending Jumu‘ah prayer and prayers in congregation just because the imam
has committed a sin, they would not be able to establish the prayer behind
anyone else. 

At-Tahhaawi (may Allah have mercy on him) said in his
‘Aqeedah (45): 

We think that we should pray behind anyone, righteous or
evildoer, among the people of the qiblah, and we should offer the funeral
prayer for any of them who dies. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him)
said: 

If it is not possible to prevent (from leading the prayer)
one who openly practices innovation or commits evil, except by causing
greater harm than the harm of his leading the prayer, then it is not
permissible to do that. Rather people should pray behind him so long as it
is not possible to pray in congregation except behind him, as in the case of
Jumu‘ah, Eid prayers and prayers in congregation, if there is no other imam
apart from him . Hence the Sahaabah (may Allah be pleased with them) used to
offer Jumu‘ah prayer and prayers in congregation behind al-Hajjaaj and al-Mukhtaar
ibn Abi ‘Ubayd ath-Thaqafi, and others, because missing Jumu‘ah and prayers
in congregation leads to worse consequences than offering prayers behind an
imam who is an evildoer, especially if staying away from the prayers will
not ward off his evil, and all it will do is mean abandoning an Islamic
interest without warding off that evil. Hence those who stay away from
Jumu‘ah prayer and prayers in congregation behind any unjust ruler were
regarded by the early generations and the imams as being among the people of
innovation. But if it is possible to offer Jumu‘ah prayer and prayers in
congregation behind a righteous imam, then that is better than doing so
behind one who is an evildoer. 

Majmoo‘ al-Fataawa
(23/343) 

What must be done is to advise these people of the obligation
to establish the prayer in the houses of Allah, which Allah has ordered to
be raised (to be cleaned, and to be honoured), in them His Name is glorified
(cf. 24:36); and of the obligation to attend them with the Muslims, and
attend prayers in congregation, and strive to establish bonds among the
Muslims, and prevent division, suspicion, and alienation among people. 

And Allah knows best.