Utah – read on. You’ll get to it.
Actually not touching is not from Chazal, it’s from the Torah (Bible), ?? ?????. Chazal made numerous statements about engaging opposite gender in conversation, idle chatter etc. The place is not here. Look up in Shulchan Aruch, ask your local qualified posek (as I wrote).
Just one note here, I think the Rambam who generally states to take the mean, middle, center path regarding all Middos and actions, deviates here regarding the separation of sexes and says “???? ???? ???? ?????? ?? ?????” (if I remember correctly). A person should distance himself EXCEEDINGLY from women.
That is being frum. (Chazal knew people’s inclination, they knew where EXTREME caution is needed.)