I would argue that Western progress in regards to LGBT rights is less related to liberal ideology, and more so a temporary byproduct of the prosperity that was gained through exploitation of the global south. We can see this progress deteriorating in real time as this prosperity is starting to subside.

Edit: Liberalism, capitalism as a whole, are fundamentally based on competition and unequal distribution of wealth. Competition means there will always have to be both winners and losers, anyone can make it, but not everyone can make it. Capitalism means that someone will go empty. And in a society comprised of many different groups of people, as soon as there's not enough for everyone, it will be the weakest groups, the minorities, who will be the first to get kicked off of the lifeboats.