So a gay Jew can't be religious?
He can be religious in 99% of his actions, but if he acts on his gay impulses then he is committing a very severe transgression in the Torah's eyes. Not entirely similar as the transgressions are viewed a bit differently, but a married man who commits adultery could also be considered religious even though he's committing a severe sin.
Let’s start with the easy ones. Then we will move on to the hugging and I and afraid to say the dreaded kiss on the cheek.
For handshaking:
Funerals - OK?
Weddings - Not OK?
Again, touching in general is considered to be forbidden and only allowed in very very limited circumstances. IF you believe it's truly necessary not to offend another and the handshake would be completely without "pleasure/affection," then you
might be able to say that in a wedding or funeral it would be ok. YET, it's still highly frowned upon and ideal to refrain.
A handshake is in itself not an affectionate act so there are times when leniency is allowed. However, all would agree that a kiss and hug in and of themselves are affectionate acts and would therefore be forbidden...