It is not permissible to offer the funeral prayer for a mushrik who committed major shirk

Firstly: 

It is not permissible to offer the funeral prayer for a
polytheist, a disbeliever or a hypocrite who is guilty of major hypocrisy.
If a person is aware of somebody’s hypocrisy or disbelief, it is prohibited
for him to offer the funeral prayer for him or to pray for forgiveness for
him after his death, regardless of whether or not he was a relative of his.

Abu Ishaaq ash-Shiraazi (may Allah have mercy on him) said in
al-Muhadhdhab (1/250): 

If a disbeliever dies, the funeral prayer should not be
offered for him because Allah, may He be glorified and exalted, says
(interpretation of the meaning):

“And never (O
Muhammad (blessings and peace of Allah be upon him)) pray (funeral prayer)
for any of them (hypocrites) who dies, nor stand at his grave”

[at-Tawbah 9:84].

That is because the prayer is offered to seek forgiveness,
but the disbeliever cannot be forgiven, so there is no point in praying for
him.

End quote. 

An-Nawawi (may Allah have mercy on him) said: 

They are unanimously agreed that it is prohibited to offer
the funeral prayer for a disbeliever. End quote. 

Al-Majmoo‘
(5/258) 

It says in al-Mawsoo‘ah al-Fiqhiyyah (41/21): 

The Prophet (blessings and peace of Allah be upon him) used
to offer the funeral prayer for the hypocrites and pray for forgiveness for
them, until the following verse was revealed (interpretation of the
meaning):

“Whether you
(O Muhammad (blessings and peace of Allah be upon him)) ask forgiveness for
them (hypocrites) or ask not forgiveness for them (and even) if you ask
seventy times for their forgiveness Allah will not forgive them”

[at-Tawbah 9:80].

So he did not offer the funeral prayer for them after that,
and he did not pray for forgiveness for them. 

If one of them died, the Muslims would offer the funeral
prayer for anyone who they did not know to be a hypocrite, but if it was
known that he was a hypocrite, the funeral prayer would not be offered for
him. 

If someone died, ‘Umar (may Allah be pleased with him) would
not offer the funeral prayer for him unless Hudhayfah did so, because
Hudhayfah knew exactly who the hypocrites were. End quote. 

When the Prophet (blessings and peace of Allah be upon him)
prayed for forgiveness for Abu Taalib after his death, Allah told him not to
do that, and said (interpretation of the meaning):

“It is not
(proper) for the Prophet and those who believe to ask Allah’s Forgiveness
for the Mushrikoon (polytheists, idolaters, pagans, disbelievers in the
Oneness of Allah) even though they be of kin, after it has become clear to
them that they are the dwellers of the Fire (because they died in a state of
disbelief).

And (Ibraheem’s (Abraham)) invoking (of Allah) for his
father’s forgiveness was only because of a promise he (Ibraheem (Abraham))
had made to him (his father). But when it became clear to him (Ibraheem
(Abraham)) that he (his father) is an enemy to Allah, he dissociated himself
from him. Verily Ibraheem (Abraham) was Al-Awwah (has fifteen different
meanings but the correct one seems to be that he used to invoke Allah with
humility, glorify Him and remember Him much), and was forbearing”

[at-Tawbah 9:113-114]. 

The same applies to the magician who seeks the help of the
jinn in doing his magic; he is a disbeliever and it is not permissible to
offer the funeral prayer for him. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked about
the ruling on offering the funeral prayer for a magician and burying him in
the Muslim graveyard after he is executed. 

He replied:

If he is executed, the funeral prayer should not be offered
for him and he should not be buried in the Muslim graveyard. He should be
buried in the graveyard of the disbelievers, and not in the graveyard of the
Muslims. The funeral prayer should not be offered for him, and he should not
be washed or shrouded. End quote.               

Majmoo‘ Fataawa Ibn Baaz
(8/111); see also fatwa no. 13941 

Secondly: 

With regard to the questioner saying: no one knows that this
person was a hypocrite or a magician or a mushrik except him, this maycome
under the heading of making hasty accusations, and what is required is to
ascertain the facts. He may have been deemed a hypocrite because of his
having one of the signs of the hypocrites, such as lying when he speaks, but
this is not sufficient to put a Muslim beyond the faith and rule that he is
a hypocrite in terms of his beliefs. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

Hypocrisy is of two types: hypocrisy in belief and hypocrisy
in action. The site of hypocrisy in belief is the heart, and no one knows it
except Allah. Therefore when one of the Sahaabah committed some error and
‘Umar said: He is a hypocrite, the Messenger (blessings and peace of Allah
be upon him) disagreed with him. 

The site of hypocrisy in belief is the heart, and it is not
permissible for one to accuse any of the Muslims, those who show loyalty to
Allah and His Messenger, of this except on the basis of clear evidence. 

With regard to hypocrisy in terms of deeds, if a person
demonstrates one of the characteristics of the hypocrites, there is nothing
wrong with saying that he is a hypocrite because of this action. So if we
see a man speaking and lying, we may say that he is a hypocrite in the sense
of hypocrisy in action with regard to this matter. And if we see him
standing to pray in a lazy manner, we may say that he has one of the
characteristics of the hypocrites, because he resembles the hypocrites by
standing to pray in a lazy manner. Hypocrisy in action is a matter that is
broad in scope, so whoever acts like the hypocrites in one of their
characteristics, is a hypocrite in terms of this action in particular. As
the Messenger (blessings and peace of Allah be upon him) said: “The signs of
the hypocrite are three: when he speaks he lies, when he makes a promise he
breaks it, and when he is entrusted with something he breaks that trust.” 

These are the signs of the hypocrite, but these signs may be
present in any Muslim people. Therefore we say that he is a hypocrite in
terms of this matter only. End quote. 

Liqa’ al-Baab al-Maftooh
(32/21) 

So it is not permissible to accuse someone of hypocrisy in
terms of belief that puts one beyond the pale of Islam, except on the basis
of clear evidence. 

And Allah knows best.