I don't particularly like any of these parties (especially the rapist protecting SWP) and I've no idea if they've got the right positions/ideas here but they are probably the 3 biggest marxist groups in the UK:
Socialist Party, June 2016 article:
LGBT liberation and socialism (first generally about LGBT, second is a specific article about trans rights)
SWP Sept 2016 publication:
The fight for transgender liberation | Socialist Review
AWL response to Morning Star's publication of transphobic articles:
Challenge trans-exclusion through debate (fucking shite response but clearly against the Morning Star).
In no way am I saying there isn't a big problem with transphobia on the left but it's wrong to say that there is nothing supporting trans rights, nothing pushing things the right direction, and wrong to make the blanket statement you started with about Marxists.
Personally I don't remember anything in Marx's works that lead to or support transphobia. I don't remember anything about trans at all, but I also can't remember anything about women's liberation which he must have said something about given the time, his political writings were focused on class / economics and most of what he wrote was about economics and not directly political, again given the time he was writing I'd not be surprised if he said nothing about trans people. Historically despite the ever present mysogyny, racism etc marxists have been supportive of feminism, anti-racism and liberation struggles in general and it makes sense to me that they would generally also be on the right side of the trans liberation struggle (but that might be more to do with how I think than reflective of wider marxists, I've definitely known more marxists who are supportive of trans rights than (openly anyway) transphobic though but again confirmation bias, me not noticing the not completely blatant transphobic stuff because I'm not trans? idk).
Other people on here would be much better than me to talk about marxist-feminist traditions but as far as I can think these are based around the idea that the liberation of women is intrinsically tied up with the class struggle and the economic nature of capitalism - that the revolutionary struggle against capitalism is part and parcel of the struggle for liberation and vice-versa. I wouldn't see any reason why TERF would rise out of that, to me it would go the other way, with the same basic analysis being applied to trans liberation struggles. There are marxists who are transphobic but I don't think transphobia rises from the marxism and I'd be interested to see the arguments they present as marxist to understand why they think it would.