Is the OP trolling here? Who writes that they are the only person who thinks some people take league tennis too seriously? Seriously? There are numerous threads about this topic.
Where I live, playing league tennis is NOT the best way to "make new friends." Most of the teams are from different towns, and there is travel involved.
A much better idea is to make friends who live by you, and who play at the same places you play.
Of all of the potential ways to "make new friends," while playing tennis, I think league tennis would be at the bottom.
Try taking a class or clinic. Sign up for a group lesson. Go to a social mixer. Talk with the pro who can probably set you up with potential partners.