Most mathematicians don't care at all about CH and among those who do not all believe that ZFC+CH is more intuitive than ZFC+not CH (really it makes no sense to believe whether it is true or not unless you believe in some platonic universe of sets, but I do maths, not philosophy), for example Gödel himself thought that the continuum could be aleph_2, Woodin's Omega logic argued the same (but this is somewhat controversial) and the proper forcing axiom also implies that the continuum is aleph_2