Stam yaynam is a rabbinic prohibition and thus we are lenient with a doubt. Anyone who disagrees is a heretic (Pitchei Teshuva YD 116:10)
As for the general question, a chumra can often lead to a kula and thus a chillul Hashem. For example, singing zemirot loudly until very late or having many guests that cause noise in the hallway late at night. Rav Yisrael Salanter railed against such people.