What about people who dont want people who are kin with specific characters from the same canon following/interacting? Example, peridot kin (steven universe) who doesnt want jasper kins following them?

My assumption is that these people are attempting to avoid others whom they consider “abusive” or with whom they have had unpleasant interactions with in the past. 

I think its sad sometimes to lump all versions of a character in the same basket and refuse to interact with them but, its their choice to avoid these people, and I advocate everyone doing what they can to maintain their mental and emotional well being. 

I’ll be honest I can sympathize because there are certain people from my past I’d be reluctant to interact with as well.

If someone doesn’t want to interact with you for any reason, you should respect their wishes. Frankly, you probably wouldn’t get along anyway, so its not much of a loss.