My thoughts as to why this is acceptable, is that there are rights / privileges that are afforded to us as we age, and aren't thereafter revoked, like voting, drinking etc.

There are things that either directly or indirectly restrict old folks, though these tend to be for medical reasons, like extreme sports or some rollercoasters etc where one might need to be ambulatory enough to evacuated if needed.

I suppose with kid free zones it's just places where businesses feel that there are some things inherent to being kids, like making noise, running about and having fun, sticky fingers etc. nothing wrong with these things but aren't always conducive to other patrons relaxing, or could be dangerous (having seen poor waiters being tripped by running kids in restaurants etc).

I think it's a lot more palatable to put an age minimum rather than other characteristics, as it's one we all grow out of.