It's often said that axioms themselves don't need to be true. What follows from axioms, however, must do so according to strict logical laws. Thus different geometrical and mathematical systems are constructed on axioms which needn't be taken as true. (This largely came to be seen to be the case in the late 19th century.)
It's not really a surprise that “anti-conventionalists” should move from propositions to concepts because, on Frege's picture, concepts are (non-spatial) parts of propositions. (Or, to use Frege's own terms, concepts are parts of Thoughts.) In that sense, a concept is simply an abstract part of a larger (as it were) abstract entity – a proposition.