You only play ARAM and a few Normals.
I personally dont like ARAM, just one straight line with towers being the only objective. There is more to do on Summoners Rift.
Now as for that when you do play on the Rift you play normals. People dont really care about normals like they do in Ranked.
Not saying people dont do this in Ranked but it does happen less i believe. Like people in Bronze are so quick to troll, int feed, afk etc. than people in Masters or Challenger because they pretty much dont care.
So your best option to avoid these people really is to play ranked and try to move up ranks to where their are less people like that and when you do get games with people like that just mute them.