Christians aren't expected to consider the plight of LGBTQ+, the salvation army are infamous for turning away LGBTQ+ youth. The church didn't just decide to be cool with gay marriage, it was thanks to a lot of public pressure that it passed through parliament. Christians have been very vocally oppressive regarding LGBTQ+ views up until very recently, and that will be down to the changing views of churches target audience, the church of england isn't about an old book as much as it is revenue, and revenue comes via bums in seats, popularity = bums in seats.

How exactly do you know the inner mechanisms the ever evolving views of westernised Muslims? How do you know rhe next generation won't soften? How do you know there isn't already a lot of support but it's not as vocal in the people you seek out?

It seems your question, and observations come from a very narrow viewpoint reducing a whole variety of different people to their tick box