Oh no he wasn’t. And he said so both publicly and privately on a number of occasions. Mind you he was up against individualist (even those who called themselves “communist anarchists” denounced democracy as the tyranny of the majority) and bomb-throwing anarchists who eventually took over and destroyed the Socialist League.
Yes of course, in the sense that Marx held that a socialist/communist society would be a state-less society, i.e., a society whose central administration would not have coercive power at its disposal (what makes such an administration a “state” as in class-divided societies). In that sense Morris too, like us, was an “an-archist”, but I think people today are deliberately calling him an anarchist to suggest that he wasn’t a Marxist.