Fixie riders are generally not welcome on roadie group rides. It's not IMPOSSIBLE to learn to ride predictably and safely on one, but most fixie riders seem completely disinterested in the discipline required.
Road riders are also not really welcome on fixed gear rides because they're unwilling to hop curbs and scare drivers to keep the flow. It's different cultures and skill sets for sure but framing it as "discipline" is kinda shitty imo.