Does The Liberal Episcopalian Church Down The Street Keep You From Attending A Conservative Baptist Church?

I've recently seen a number of Catholics using a bad line of argumentation that I've never understood. We're told that a reason for not being Protestant is that there's so much diversity of belief in Protestantism. We're told of how bad it is to be associated with an Episcopalian church that accepts homosexuality or a Methodist church that ordains women, for example.

Let's say that you're a college student looking for a church to attend near your campus. You think that the beliefs of a Baptist church nearby are correct, and the church seems to be healthy in other respects. And there's an Episcopalian church down the street from the Baptist church. It contradicts much of what you believe. It's significantly different from the Baptist church. Does the fact that both churches could be classified as "Protestant" prevent you from attending the Baptist church?

The Protestant classification is secondary. Similarly, we could refer to all Western churches collectively as "Western Christianity", for example, yet I don't know of any Catholic who wants to leave Roman Catholicism because being part of Western Christianity associates him with homosexual Episcopalians and female Methodist pastors.

In many areas of life, not just in religious affiliations, we're associated with larger movements that include elements that we don't support. But an association can be so distant that no reasonable person should conclude that you're showing support for something by being associated with it in that distant manner.

One of the problems with the Catholics who use arguments like the ones I've described seems to be that they don't give much thought to how the same sort of argument could be used against Catholicism. They might refine their objection so as to exclude Catholicism from the objection, but then they're changing their argument, and we would have to ask what significance the new objection has. A lot of Catholics, including converts to Catholicism who have been given many platforms to speak from, don't seem to have given issues like these much thought, even after being Catholic for years or decades.