How do you define these terms? According to Gallup self identified Liberal Republicans have a 76% approval rating of Trump whilst self identified conservative Democrats have only a 22% approval rating of Trump, so the answer is the former.
that's kind of the opposite of what i'd imagine
The majority of conservative Democrats are African-American or Latino--so naturally they don't care for Trump.
Most of them are far from being "real" conservatives, first of all - on economic issues. Usually their "conservatism" is limited by few social issues (abortion, LGBT-rights or something similar). So, as i said few years ago - i am not aware of really "conservative Democrats" or really "liberal Republicans" on level higher, then local, NOW (unlike even 20-30 years ago)..
Well OP has failed to give a coherent definition of the terms “Liberal Republican” and “Conservative Democrat” so until he delivers we can only provide broad interpretations based on the data we have... 
Sure. But - to give few examples - "conservative Democrat" to me is NOT a person like Manchin or Cuellar (both are "centrists", judging by their voting records and ratings by ideologically "pure" organizations like ADA or ACU), but someone like former North Carolina Senator Sam Ervin (or Alabama's James Allen and Richard Shelby) or former Mississippi congressman and governor John Bell Williams (minus open racism of course, which is not so relevant now as it was then). And i don't know present day Democratic officeholders with so conservative views. The same with "liberal Republicans": for me these are people like Joseph Javits, Charles Mathias and Charles Whalen - and, again, i don't know a single Republican officeholder with similar views.
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