What security updates would you foresee being necessary for a traditional BluRay player? Perhaps I'm not being creative enough, but I can't think of what a hacker would accomplish.
Other than allowing the player to read pirated BluRays, I guess, but that's not the user's problem.
Maybe making the player part of a DDOS botnet? That's all I can think of.
The only consumer electronic in my house I allow to talk to the internet is the AppleTV. Nothing else is allowed on the router. Not the TV. Not the disc player. Not the refrigerator. Not even the "smart" thermostat.
I don't know about security per se (as others have mentioned a dumb player doesn't need internet), but I could very easily see a decoder bugfix or something to do with i/o error conditions or mishandling some particular kind of disc...
Other than allowing the player to read pirated BluRays, I guess, but that's not the user's problem.