With the exception of one other time I can remember, the many other churches I visited were all on my mission. It's not encouraged for missionaries, but it's not taboo either because you're getting your brand out there and it's as good as spending that same time knocking on doors or spending another two hours at a member or eternal investigator home. Of course, our motivation wasn't always pure, it was more like, "let's see what these weirdos got going on," or poking the bear, rather than serious interest in finding people to teach. I would say that 90%+, if a missionary is visiting another church, it's ironically.I know LDS missionaries visit non-LDS churches.
It's absolutely taboo to visit another church as a regular member. There's no rule against it I suppose, and if you have a cousin getting some rite of passage done I think most would understand, but just visiting another church to see what they believe? It's a very strange thought. I don't think there needs to be a rule because nobody would ever consider it. As a child, I recall going to breakfast and having pancakes on a Saturday at a Baptist function because we were invited by our Baptist neighbors. I recall it just a little because it made such an impression, because it felt so weird being around all these people who were just ever-so-slightly different than we were, having breakfast just like we would.
We only went, of course, because my dad was a missionary (either as a stake missionary, a normal member role, or just of his own accord, something Dan, Kiwi57, and Lou have never been) and thought if we went to their church function maybe they would come to ours? Of course they didn't, as conservative as we were as a family, they were even more so.