It shouldn't matter, but it does. I don't think anyone will give you flack for showing up to any gig with a P bass! But people might look at you weird if you showed up to a country, or even punk, indie, metal, etc. rehearsal with a Bootsy signature model.
It's just like having tattoos. Even though the culture has changed a bit over the years, and the stigma isn't as strong as it used to be, If you decided to get sleeved up with tattoos and get them on your neck (what I like to call 'job killers') you have to go into it assuming that, although it's not right, people are just going to judge you differently. Trust me, I work as a registered nurse in a children's hospital and have sleeves, and some facilities were not cool with it, while others make me cover them up, and then there are a few that could care less!