I'm somewhat of an expert in this field. /silly
I have a LOT of f/os, so I do bumb into people with whom I share a couple from time to time, and while I don't much interact with the community, I still encounter others who self ship with them! Usually it goes something like this:
Oh, they like [this character]! That's nice!
*Blocks*
You don't have to block anyone who shares your same popular f/o, that's just what works best for me. It depends how you feel about interacting with others who have your same f/o and, for me personally, it's not something I'm particularly comfy with simply because there's so much attached to these characters for me. Some of them motivate me to get in the shower, some of them make me smile until my cheeks hurt, some of them help me get out of bed in a morning - heck, some of them are just there for funsies, but they make me happy so they stay there. A lot of them were inflicted upon me by my best friend @magicmugships and I ended up getting too attached to let them go, which is how they built up like they did... I've also been a self shipper since I was a kid, so it's a bit like when you accumulate a bunch of DVDs over the years but you keep them all just in case you want to watch any of them one day!
That to say, while in my case it perhaps narrows down my friendship options within the community, I'm okay with that because I prioritise my own comfort over having more friends when I've already got a wonderful best friend who knows my boundaries and with whom I don't have any overlapping f/os. That said, if I ever was to seek out new friendships in the self ship community, I'd still be cautious even if I managed to find someone who didn't share any f/os with me, because part of the reason we get along is likely to be that we share the same interests and type. While we don't have any overlapping f/os now, we potentially could in the future, and I just don't have the time or energy to fight about that sort of thing.
Being a non-sharer with a massive collection f/os (against my will) isn't really an issue for me simply because I already have a super-duper close self shipping friend who I get along with perfectly most of the time and, again, who knows my boundaries. Outside of events like F/Ovember, I don't really go out of my way to interact with the wider self ship community specifically to avoid this issue, even with my block strategy, and also because I have some f/os that might (understandably) piss some people off but I stand with my cancelled wife. Block and move on is a great solution for most anything and anyone that makes a person uncomfortable on the internet.
If you made it this far and you're encountering the dilemma of self shipping with a popular character but also being a non-sharer. I truly recommend blocking people who share your f/o(s) and moving along. Does it take some potential friends out of the pool of people in that fandom? Yes, but if you place your own comfort over the desire for new friends, it works flawlessly.