I heard something very astonishing. That a Rabbi during a Torah class said that you should not kiss your children after they have been playing vigorously and hard. Could that really be true? Why?

The above is likely based on a rule of Shulchan Aruch (Y.D. 116: 4) and Yerushalmi (Terumos 4), that human sweat is deadly poisonous with the exception of the sweat on the face. Taz (ibid 2) mentions as a way for remembering the above the verse (Bereshis 3: 19) “By the sweat of your brow you will eat bread.” Indeed, Psokim Uteshuvos (116: 2) and others quote the above as a source of not kissing the body of a sweating person.