His boss gave him the choice between reducing his beard or leaving the job

Firstly: 

Shaving the
beard is haraam, as is shortening it and reducing it, because of the
evidence which shows that it is obligatory to leave it alone and let it
grow. 

It says in
Fataawa al-Lajnah al-Daa’imah (5/133): Shaving the beard is haraam
because of the saheeh ahaadeeth and reports that have been narrated
concerning that, and because of the general meaning of the texts that forbid
resembling the kuffaar, including the hadeeth of Ibn ‘Umar, which says that
the Messenger of Allaah (peace and blessings of Allaah be upon him)
said: “Be different from the mushrikeen; let your beards grow and trim your
moustaches.” According to another report: “trim your moustaches and let your
beards grow.” And there are other, similar ahaadeeth. Letting the beard grow
means leaving it as it is and not shaving it, or plucking or cutting any
part of it. Ibn Hazm narrated that there was scholarly consensus that
trimming the moustache and letting the beard grow is obligatory, and he
quoted as evidence a number of ahaadeeth, including the hadeeth of Ibn ‘Umar
(may Allaah be pleased with him) quoted above, and the hadeeth of Zayd ibn
Arqam, according to which the Prophet (peace and blessings of Allaah be
upon him) said: “Whoever does not trim his moustache is not one of us.”
Classed as saheeh by al-Tirmidhi. It says in al-Furoo’: According to
our companions – the Hanbalis – this indicates that it is haraam. 

Shaykh
al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: The Qur’aan,
Sunnah and scholarly consensus indicate that we are commanded to be
different from the kuffaar and that it is forbidden to resemble them in
general terms, because resembling them outwardly may cause us to resemble
them in attitude and doing blameworthy deeds and even in beliefs. It
generates love and friendship inwardly, just as inward love generates
outward resemblance. Al-Tirmidhi narrated that the Messenger of Allaah
(peace and blessings of Allaah be upon him) said: “He is not one of us who
imitates people other than us; do not imitate the Jews and the Christians.”
According to another report: “Whoever imitates a people is one of them.”
Narrated by Imam Ahmad. And ‘Umar ibn al-Khattaab rejected the testimony of
a man who plucked his beard. 

Imam Ibn
‘Abd al-Barr said in al-Tamheed: It is haraam to shave the beard, and
no one does that but effeminate men, meaning those who imitate women. The
Prophet (peace and blessings of Allaah be upon him) had a thick beard,
as was narrated by Muslim from Jaabir and in other reports. And it is not
permissible to remove anything from it because of the general meaning of the
evidence that shows that that is not allowed. End quote. 

Shaykh Ibn
Baaz (may Allaah have mercy on him) was asked: What is the ruling on one who
makes the ends of his beard even? 

He said:
What is required is to leave the beard alone and let it grow, and not to do
anything to it, because it is proven that the Prophet (peace and
blessings of Allaah be upon him) said: “Trim the moustache and let the beard
grow; be different from the mushrikeen.” Saheeh – agreed upon. Narrated from
Ibn ‘Umar (may Allaah be pleased with him). And al-Bukhaari (may Allaah have
mercy on him) narrated in his Saheeh from Ibn ‘Umar (may Allaah be
pleased with him) that the Prophet (peace and blessings of Allaah be
upon him) said: “Trim the moustache and let the beard grow; be different
from the mushrikeen.” Muslim narrated in his Saheeh from Abu Hurayrah
(may Allaah be pleased with him) that the Prophet (peace and blessings
of Allaah be upon him) said: “Cut the moustache and let the beard grow; be
different from the Magians.” 

All these
ahaadeeth indicate that it is obligatory to leave the beard alone and let it
grow, and to trim the moustache. This is what is prescribed in Islam, and
this is what is obligatory, as taught and enjoined by the Prophet
(peace and blessings of Allaah be upon him). This is following the example
of the Prophet (peace and blessings of Allaah be upon him) and his
companions (may Allaah be pleased with them), and differing from the
mushrikeen, and avoiding resembling them or resembling women. 

With regard
to the report narrated by al-Tirmidhi (may Allaah have mercy on him) which
says that the Prophet (peace and blessings of Allaah be upon him) used
to remove something from the length and breadth of his beard, this is a
false report according to the scholars, and it is not a saheeh report from
the Prophet (peace and blessings of Allaah be upon him). Some people
insisted on using this hadeeth as evidence, but it is not a saheeh report,
because its isnaad includes ‘Umar ibn Haroon al-Balkhi, who is accused of
lying. 

So it is not
permissible for a believer to follow this false hadeeth, or to use as a
concession that which was said by some scholars, for the Sunnah is binding
upon us all, and Allaah says (interpretation of the meaning): 

“He who
obeys the Messenger (Muhammad), has indeed obeyed Allaah”

[al-Nisa’
4:80] 

“Say:
Obey Allaah and obey the Messenger, but if you turn away, he (Messenger
Muhammad) is only responsible for the duty placed on him (i.e. to convey
Allaah’s Message) and you for that placed on you. If you obey him, you shall
be on the right guidance. The Messenger’s duty is only to convey (the
message) in a clear way (i.e. to preach in a plain way)”

[al-Noor
24:54] 

“O you
who believe! Obey Allaah and obey the Messenger (Muhammad), and those of you
(Muslims) who are in authority. (And) if you differ in anything amongst
yourselves, refer it to Allaah and His Messenger, if you believe in Allaah
and in the Last Day. That is better and more suitable for final
determination”

[al-Nisa’
4:59]

And Allaah
is the Source of strength. End quote from Majmoo’ Fataawa al-Shaykh ibn
Baaz (4/443). 

Secondly: 

It is not
permissible for your boss to order you to reduce your beard, because this is
an order to commit sin, as explained above, and you have no right to obey
him. Rather what you must do is be patient and explain the shar’i ruling to
him. If he insists on his opinion, and letting your beard grow means that
you will lose your job, it depends on your situation and your work. If you
can find another job, then leave this one, seeking the pleasure of Allaah.
If you cannot find another job, then we hope that you will be forgiven if
you reduce your beard, because the scholars have stated that it is
permissible to do a haraam action in causes of necessity and extreme need,
so long as you limit yourself to the minimum of reducing it that will please
your boss. Allaah says (interpretation of the meaning): 

“So keep
your duty to Allaah and fear Him as much as you can”

[al-Taghaabun 64:16]

See also
question no. 70319. 

And Allaah
knows best.