Do you know anything about the law regarding us as admins and running a Rust server?
A guy asked me if this was legal if there might be playing underage kids on my server.
I think it is not my task to find out if the players are old enough to buy the game legally and play on my server or not. Although I wouldn't know how to check that.

But are you aware of these things? Is this legal for us?
He mentioned EULA.

You can't exactly ask people for ID when they join, and Steam profiles don't exactly show dates of birth either. There's literally no way you can effectively enforce this, and the onus is not on you to do so. 

He would probably be the only person who has every fully read an EULA !!, If this was a condition for server owners to be aware of and to police  you would think there would be a "are you over 18" warning for you to confirm before you play, but that is not on any official FP run servers so it is not something to worry about,

Well and keep in mind that game rateings for diffrent countries vary... What might be acceptable in the USA might not be in China (just using examples)... I mean myself host servers in both the US and UK.... in the end its not your responcibility to watch someones kids... if there parent lets them play thats on the parents.. not you as a server owner. I mean if you are really worried and dont want to chance it then run a whitelisted only server and requier some sort of verification of age... tho I can see that having its issues as well.

The Rust EULA states that anyone who is using purchasing the game must be at least over 13 years old, and requires parental agreement if they are under 18. This is up to Steam or Facepunch to enforce, not server hosts.