Protestants generally like to try and convert people. With Catholics, it’s…pretty predictable, let’s call it that. It largely depends on the Reformers being right about a few things. But then with the EO, we wonder where are your Reformers? Without that, we struggle to find reasons to ask EO Christians to convert.
A fair number of Protestants do try to come up with those reasons. We’d like to convert everyone, after all. But when the Reformed history is (in effect) taken away, it’s much harder. This can wind up looking like arbitrary favor or special treatment that’s given to everyone except western Catholics, but there is a real reason behind it. Any time a Protestant tries to convert someone from a more ancient form of Christianity, we need a Reformation that we can make a positive argument for. Any time we don’t have that, we’re less likely to try and very unlikely to do much even when we do try hard.
When dealing with western Catholicism, particularly the Latin rite, that’s the only time we get what we need. Reformation equals critical leverage, and we get that nowhere else. If it was there, some Protestants would use it. Not all, but anyone who goes off on Catholicism in really squicky ways would go off on similar things in similar ways, I promise you that. A greater amount of ignorance along with less familiarity with friends and family who personally show us good qualities in that particular expression of Christianity would probably make the situation even worse by comparison. But we don’t have the opportunity to do the same things, and that is why it doesn’t happen.