Answering your particular case:
Your football skills (especially game vision, defensive skills) should match your leadership ambitions. Apart from the seniority in the team or leadership qualities, these are the skills players need to have to captain their teams. If you are in possession of these skills and if you create chances for your teammates to play (which is very important in street football), your teammates will love to have you as a leader, motivator, or someone who tells them where, when or what to improve.
Answering your general question:
In my personal experience as a frequent player, “what happens on the pitch stays on the pitch” is only applicable if you are fiendsfriends outside football too. E.g, if it was something else that connected you: your neighborhood, college, school, work, etc. but not the football itself. If it's not the case, I'm afraid, the great answers given on ips.se still hold.
Your football temperament is very close to mine. I have couple of unpleasant memories from the times when while being extremely emotional and passionate about the result or small game details I have ruined the game for my teammates and opponents.