I believe that the following is accurate:
1. D’oraisa you absolutely do not have to wear tzitzis (assuming you’re not wearing a four-cornered garment). Wearing a four-cornered garment is entirely optional.
2. There is either an established minhag or a din d’rabanan (I’m not sure which) that Jewish males SHOULD wear a four-cornered garment, thus necessitating tzitzis and, ultimately, being mekayem a D’oraisa. It is this that certain rabbis (I think R. Moshe Feinstein has a teshuva to this effect) are trying to protect when they tell people to keep their tzitzis on when playing ball in the hot summer months.