I've been called to collect my kids from creche/kinder when they have had a temp or been lethargic or miserable IYKWIM.

The snot hasn't been an issue but then my kids really aren't snot monsters if that makes any sence. Perhaps they make a judgement based on how much snot is running out of the childs nose. I would be inclined to think that a wipe here or there woudn't be a problem but if the carers are constantly wiping it then that's when they decide they should be at home.

FWIW if they were too fussy about runny noses there would be days when all the kids were sent home.