What Larissa said! From a shrine-maker's perspective, I say: GO FOR IT. For me, a shrine is a dump and storage for your thoughts - things you don't get to word vomit about in other places, and especially a
collection of all your thoughts pertaining to the subject. That includes these "off-topic" things, since it wouldn't feel "complete" to you without them.
And really, from the perspective of a visitor, those essays are very entertaining and interesting to read. It can lead to learning new things, looking at things from a different perspective, or discovering related things. It needn't even be in essay-format: a series of pictures and lots of yelling, for example, do the job too. Not to mention that kind of essay really is what adds a personal touch to the shrine: a product of things that you have thought about, consumed or been through.
Personal example: The
parallels page on my Dream Saga shrine. I drew comparisons to a bunch of series that are similar to Dream Saga in one way or another, and that was really fun. Things I had always thought about, but never really took the time to formulate in words before, some of them things that I wouldn't ever shrine or dedicate a full essay to - it's nice to "get them out of my system" somewhere.
I've also always had a weak spot for "look-a-like" and similar comparison pages in general, and I love how there are multiple ways to go about writing such pages. (They're one of the main reasons I really wanted to get into shrining ahaha...) Examples:
I can't think of many examples of pages outside of this category though - or maybe everyone just does such a great job weaving the respective topic into their shrine that I don't remember them as "tangential" haha.
Some people also cover elements that aren't exactly "tangential" in the sense of "only I would have made this connection!" - elements that may have influenced a character's design, for example. It's common to cover those on Pokémon shrines in particular, but not necessarily on other sites since there are plenty of other things to talk about already, things that are more important to the subject in question and already take up a lot of time to write. But I do like learning about those things that are a bit "further away", too, and Megan's shrines usually introduce me to new things: types of dances on
Shatter Me, for example.