To Carnap being a realist is no more than opting for the vocabulary/language of realism. According to Carnap's
principle of tolerance there are no truth-relevant arguments in favour of realism and against a form of anti-realism.
From his empiricist stance, whether one chooses a realist or an anti-realist vocabulary/language does not
make any difference to any truth-relevant, thus empiristic, problem and hence to the theory formulated in this language. The question of whether realism or anti-realism is correct
is a pseudo-problem (Scheinproblem).
Quine does not distinguish between language/vocabulary (analytic sentences) and theory (synthetic sentences). The choice of language/theory is based on the precision of its predictions. Physics, the paradigm of a successful theory, makes claims for reality. Quine does not see any reason to disdain "exists" in a theory that works as well as physics. In fact, one might say that the success of a language/theory like physics with respect to predictions exactly stems from the fact that it is very precise when it comes to claim the existance
of things. Hence, there really is matter in space-time.
To Carnap, the question of what language to choose is an external question. The question of what sentences are true, thus of what theory we accept in this language, in turn, is an internal question. As for Quine language and theory are inextricable, there are only internal questions. "We are like sailors who must rebuild their boat on the open sea, without ever being able to put into dock and
reconstruct it from the best components." as he quotes Neurath at the beginning of Word and Object. According to Quine, philosophical questions must be treated
as scientific questions and thus internally. According to Carnap, (most) philosophical
questions are external pseudo-questions.