About "how to play songs that I don't like", I believe that people that do that have a further goal behind, such as money, friendship, simple practice, or whatever it is.
So to me it seems you have to find a goal that makes it worth going through such inconvenience.
Now, personally, I don't play music that I don't like and above all
with musicians that I don't like, and that despite being a professional musician, since my main goal is to play what I think is good music with good musicians, so doing the opposite would go against
my objective and principles.
But I have a question TO YOU about the
songs that you like and those that you don't, in essence there is
not really stylistic difference between them to me, it seems strange (and not at the same time), it´s all rock/pop back beat music, many times very similar and/or same tempo... basically you have to play the same thing in all of them.
Your examples of LIKE/DISLIKE:
LIKE 1)
DON´T LIKE 2)
Are you sure they are too different?
P.S.:
To me something different would be (I´m trying to restrict myself to music with singers):
A . Med Up Jazz:
B . Mostly 3/4 Fusion
C . Up Tempo Samba
ETC. x 1000, the list and styles would be endless!