Historically Judaism was an actively proselytizing religion as well.
I'm going to need some sources about that.
Judaism takes its roots in several ethno-religions. Ethno-religions, by definition, do not proselyze outside of a specific ethnic group.
I know some people thought that the size of the jewish communities inside of the Roman empire, or such things as "Beta yisrael" or jewish Khazars (and other examples) could only be explained through proselytization, but they have been proven wrong many times. It's true that some states and some people decided to convert to judaism at certain point, but they didn't do it because of jewish prozelytization (it's usually political and/or theological, and motivated by internal forces, not by external jewish missionaries - the Khazars converted because they didn't want to choose between christianity and islam, but they didn't want to be pagans either).
And the jewish communities inside of the Roman empire are quite a complicated matter given the variety of jewish sects, and the fact that "jewish" was both a religion and an ethnonym. Just to give an example, the jewish community in Alexandria, Egypt was very hellenized and quite open religiously, so you were jewish as soon as you were part of the jewish community basically ("inside the walls" conversion).
But while jewish communities sometimes grew thanks to a very permissive conversion rules, they were never proselytizing in the sense of sending missionaries to convert people. Except in the very specific case of a group of people already considered as jewish, but following the wrong sect/religion (in that case it's perceived more like a return to judaism).