If you think that you're feeling pressure then your probably right
On the other hand, I think that the "pressure" most people feel is primarily their own responsibility. Mind over matter - I don't mind, so it doesn't matter.
I don't mind cross-training at two or more unaffiliated clubs on a regular basis. I am not concerned with belt colour, rank or grading. I just want to train. But the trouble is: these unaffiliated clubs would really mind my "dual-membership".