Is global acceptance of the LGBT community possible?

Of course, I do believe that someday, the world will be a place where sexuality, gender identity and race will all be on a par with things such as eye colour or hair colour, or height; it's just that sometimes I feel that there are some countries (particularly the really extremely religious ones in Africa and the Middle East), where, worse than there being no change in societal opinion - which is bad enough - people are becoming more homophobic. Evidence of this includes Russia passing a bill that bans gay pride for the next 100 years, which was, by some miracle that I shall never understand, upheld by a judge! Also, sticking with Russia, anti-gay protestors are suing Madonna for $10.5 million as a result of her violating the "no gay propaganda" law that passed recently as well.
In addition, people are executed every year in Africa and in the Middle East for consensual homosexual behaviour, and public opinion in those regions of the world seems to support this sort of legislation.

Ok, so the point of this topic is more about how, rather than whether, these parts of the world will eventually come round to a more liberal way of thinking on the matter of sexuality...

Will it come from international pressure?
Will increased discussion make the subject less taboo, and, as such, eventually, more accpetable?
Will future leaders be bold and pass legislation before the public demands it, or will legislation follow societal evolution on the subject?
Or maybe something else?

Also, does anyone think that there is anything we can do to help the cause?

I know in the West, most LGBT people are focused on marriage equality and adoption rights etc. but there is no doubt in my mind that the West WILL get there - and soon... within the next few decades, i'm sure... i just wonder how we will be able to change the hearts of people who have not changed their stance for the better, and have stood firm in their original beliefs while the rest of the world has moved on.

Uganda or another nation cracked under pressure and shelved their "Kill the Gays" bill due to international/global outcry. If that's possible, I think it's possible that with time acceptance of the LGBTQ+ community will be a global thing. However, despite my optimism, I don't see such a radical change happening within my lifetime, with how religious and conservative many parts of the world are.