I wish we could reclaim the word liberal in the old-fashioned sense of liberal political theory, not the modern sense of "letting it all hang out", or even worse, used as a synonym for libertarian by people who are too ill-informed to know the difference.
Properly understood, it's not clear to me that a liberal feminist would or should be "pro sex-work." If you were to take Rawl's "initial position" type thought experiment as the starting point for your liberalism, for instance, you could argue along these lines: "Well, we know this society we're going to create from first principles and dropped into will have inequalities, and I might end up at the bottom of the heap. Forget the mythical 'happy hooker' for a moment - how would I feel about finding myself as the person who had to have sex for money with people I found repulsive simply in order to feed and house my children?" A liberal, at this point, might well decide that this was the point at which "maximising utility" for society as a whole might require a blanket ban on prostitution, just as it would favour a blanket ban on selling your organs.
Similarly, liberalism has often involved very robust defences of free speech and of freedom of belief, and being allowed to get on with what you want to in the private sphere but having to balance your "freedoms" against other people's "freedoms" in the public sphere. Which would seem to me to handle the trans debate perfectly - a liberal would defend to the hilt the right of anyone born male to wear a dress, lipstick, call themselves by a woman's name - but when it came to, say, open plan, communal, single sex changing rooms or prisons or shared overnight accommodation, the transwoman's desire to be "treated as a woman" would have to be balanced against the women's desire not to be in an enclosed space where they were vulnerable with a person with a penis.