When people are being toxic I mute them, then tell them that I've muted them in team chat. I do this so that my other teammates don't think I'm ignoring callouts.

Half the time they will go into chat and ask the people on the other team to report me and make up some stuff when they realize that I'm not going to give them the reaction they want. A lot of the time toxic people are with their friends, so their friends will tell the other team to report me too.

If someone on the other team is being toxic, their teammates will report them. You don't have to. You also don't know who is the one actually being toxic since you don't get to see team chat or listen to their voice chat.

TLDR; you don't know the situation, most of the time when someone says "report my teammate" that person is the toxic one. Let their own team report them.