I don't really understand the 'relative discrimination and suffering' argument, as an argument. What's the purpose of it?
Is LGBTetc the 'coalition of all those who are discriminated against'? Is it 'the coalition of all those who feel marginalised by mainstream society and wish to empathise with and support each other'? Well, clearly not, as in either case it would encompass BAME, disability, immigrant, impoverished and other groups who are discriminated against and marginalised.
It's not the group of about people discriminated against because of their sexuality, or their bodies, appearance, ideas... what is the common factor?
If one group believes itself to be both distinct and more discriminated against than anyone else, surely the reasons for that discrimination must be something to do with the thing about that group that is distinct. So, keeping that group distinct and its message clear, for the purposes of political campaigning, would be the obvious thing to do. Any other course of action will dilute both the group's distinctive characteristics and its special claim for consideration.
I can see there's an argument for piggy-backing on a larger, well-established group, which has already achieved a lot of social and political change. But, doing so when you believe that you and the issues you face are distinct from those faced by any other group, just buggers up your USP / special claim and causes confusion.
Just musing on OP's question. Of course people can organise themselves as they wish and don't have to explain themselves to anyone else. That I don't get it doesn't matter at all.