Player would be protected by the team. So in theory the fan could sue in civil court but good luck.

This is baseball but I'd imagine it's the same for any professional sport. https://www.justbats.com/blog/post/penalties-fines-for-running-on-a-baseball-field/ and with examples: http://sites.law.duq.edu/juris/2014/10/07/legal-consequences-of-rushing-the-field/

It's straight up illegal to run on a field. I don't see why it would be any different for a player to tackle them vs a security guard doing it.