I bring my bag, but I leave it off to the side where there's a rack/area for it. (The rack is on the gym floor).
I train Powerlifting style training, so I have my belts, wraps, Slingshot, "foam board press" and things like that.
I take things out as I need them.
But we do have a couple, who bring their giant bags, sprawl them all over the gym floor (both of them) and you need to watch out and step around them, etc...