Does a Muslim woman have to cover her face in the presence of a gay man?

Homosexuality is a great and abhorrent evil which is
off-putting to those of sound human nature. One of those of sound nature
said: Were it not that Allah, may He be glorified and exalted, told us the
story of the people of Loot in the Qur’aan, I would never have thought that
a male could be intimate with another male. Hence both the one who does it
and the one to whom it is done to be executed. This has been discussed
previously in the answer to question no.
27176. 

Secondly:

It is not permissible for anyone to accuse another person of
doing the action of the people of Loot unless that is proven with acceptable
shar‘i evidence, such as a confession or if the action is witnessed by four
witnesses of sound character. If a person transgresses against another by
accusing him of this immoral action, which is a slur against his honour, and
he has no proof, then he is making a false accusation and deserves the
appropriate deterrent punishment. The obligatory hadd punishment in this
case is eighty lashes. Allah, may He be exalted, says (interpretation of the
meaning):

“And those who accuse
chaste women, and produce not four witnesses, flog them with eighty stripes,
and reject their testimony forever. They indeed are the Fâsiqûn (liars,
rebellious, disobedient to Allaah”

[an-Noor 24:4]. 

Thirdly:

The Muslim woman is required to cover herself, including her
face and hands, in front of non-mahram men. If it is known that a man is an
immoral evildoer, then covering herself in front of him is even more
emphasised. 

The Muslim woman should be more cautious with regard to this
evildoer than others, and should take care to ensure that there is no
meeting or conversation between them. 

For more information please see the answers to questions no.
11774,
21536 and
6991. 

And Allah knows best.