You get to decide what's important to you. If you're more concerned about being allowed to wear a particular color of belt than the opportunity to learn something new, then I guess that must be your top priority.Thats how it should be. If a person walks in with a BB from somewhere else you say ok no problem you just have to learn the curriculum. I guess thats why I never took a BJJ class. Cause they want you to start as a white belt and I always say no.
LOL!
I have black belts in 3 different arts. If I was to attend a class in an art I wasn't ranked in (like TKD), I wouldn't consider wearing anything but a white belt - or whatever the equivalent rank is for that art. (Even though I do have some skills which would likely be transferable to the new art.)
A black belt (or any other rank) isn't a badge of your worth as a martial artist or a person. It's just an indicator of having met certain specific requirements within a particular art according to the standards of a certain instructor/organization. It has no meaning outside that context. A BJJ black belt doesn't mean the same thing as a TKD black belt doesn't mean the same thing as a Modern Arnis black belt. Wearing a rank emblem outside of the relevant context is pointless and likely to lead to confusion.