If they only single out homosexuals and not other "sinners" they are engaging in an arbitrary exclusion, regardless of their own flawed opinions on it.
Actually no...
If they single out ONLY homosexuals and not other sinners who routinely, on a daily basis, continually and routinely perform the same sin and not only perform it but perform it without an attempt to repent for it nor attempt to NOT perform that sin, then you're right.
For example, if they had a member whose a rapper that uses the lords name in vein in every one of his songs, sings those songs on a weekly basis, and repeatedly states he doesn't care about using it and doesn't repent for it then, then you'd be right.
However, there is a difference in someone who sins, repents for that sin, acknowledges its a sin, and works to not sin and someone who indulges in a sinful lifestyle every moment of every day through his thoughts, actions, and way in which he identifies himself and proclaims no repentence or asks for no forgiveness from god for it but instead indulges in it as a good thing.
If they exclude all sinners, the group can't exist because all people are sinners accoring to Christianity. If they only exclude unrepeneatent sinners, they need to be consistent in their application of that. Are they excluding people who have ever lied, coveted, adultered failed to keep the sabbath holy, dishonored their mother and father and that haven't made any attemtps to make ammends? Then they aren't being arbitrary.
As I said, they could easily state "Anyone who wantonly and repeateldy engages in a sinful lifestyle daily with no repenetence for that act or attempt to not engage in that sin" and it would be hard pressed to find much else that it would fit. Adulterers? Unless that person is CONTINUALLY performing adultry, someone that has done it once would not fit. Someone that coveted? Again, they'd have to do it continually, and they'd have to do it each time without repetence and with an attitude or statement that its perfectly acceptable to covet things. And on and on.
I get your point, I understand YOUR view of the hypocrisy of it, but YOUR view in and of itself is arbitrary as well based on what you view as logical.
To me, while I don't agree with it, its entirely logical to suggest that someone who continually performs a sin, regardless of what that sin is, without any regret/repentence/asking for forgiveness and more than that actually claims its a good thing and makes no endevours to stop sinning is someone living a "Sinful lifestyle" where as someone that commits sins, but repents from thos sins, acknowledges those sins are wrong, and works to not sin is not living a "Sinful lifestyle".
Everyone sins, sinning is part of being human. The difference in this case is how one reacts to their sins...do they revel in it, are completely unrepentant of it, and plan to continue doing it routinely rather than work to stop it....or do they recognize it as a sin, repent, and attempt to lesson their sinful ways?
Yes, I would say if they said "no one living a willfully sinful lifestyle" may enter and its somehow proven that someone else doing a different sin fits the same bill and they let them in...THEN its arbitrary. But if you can't find another situation where someone was allowed entrance while continually and repeatedly engaging in a sinful act that they proclaim as not sinful and instead perfectly okay and that they brazenly promote and proudly proclaim a desire to continue doing rather than work to fix, then there's nothing arbitrary that I see in it.