There are a few examples frequently offered for the rule "עשה דוחה לא תעשה":
Someone whose garment has four corners and linen can nonetheless put wool tzitzis on it. This is unlikely nowadays, when we don't wear four-cornered garments. (Anyway, I wonder whether it applies if we don't have t'cheles, which I assume we hold, at least l'chumra, is the case today.)
The obligation of mila overrides the prohibition on cutting tzaraas off of one's body in case they happen to coincide in time and location on the body. Again, irrelevant nowadays in the absence of tzaraas diagnosing.
Are there any nowadays-practical examples of עשה דוחה לא תעשה?