I'm not a Catholic myself, but I taught at Catholic universities for several years.  I think Francis is more LGBT-accepting than his predecessors, and on a visit to the US, he had a well-publicised private meeting with a former student and his husband.  At the same time, it's very hard to change the direction of a large institution with hundreds of years of tradition behind it–assuming he wanted to.
That said, the Catholic church is not as monolithic as some think: Â At the local church level, some parishes are very diverse and inclusive; others are quite the opposite.
There's also a lot of variation by country/region: Â I worked in Sydney, Australia for a while, and while the Anglican church there seemed quite homophobic, the Catholic church (at least the cathedral and its music programme) seemed very inclusive and welcoming. Â That's a contrast to the US, the "Episcopal Church" (part of the Anglican Communion) is very LGBT-inclusive.