Do the Shi'a believe that if more than 3 hairs of a cat get on their clothes their prayers are not accepted? If so, what is the evidence supporting this position?
The number is not mentioned, but in fact, if it's like a bunch of hair then prayer in these clothes should be avoided.
see:
Question: Does cat hair affect ones prayers?
Answer: If there is a few cat hairs (one to three) on a person's body or cloth, his prayer is in order but if there are more than that, his prayer becomes void, as an obligatory precaution.
https://www.sistani.org/english/qa/01130/
see also:
https://www.islamquest.net/en/archive/question/fa745