Why is it illegal to put out word for DnD players who aren't high schoolers?

It isnt illegal, the store owner is being a douchebag.  You can print this out and take it over to show him.

IT would not be "illegal", but you might want to consider using the word Adult in your post.  Like Player position open for Adults, would take care of it.  You could also "consider" teens, but not select any.

Okay, here we go:

First of all, why do you say that high-schoolers aren't mature enough? When I was twelve, I was studying quantum mechanics as a hobby, knew all the ins and outs of sexuality, and had already identified myself as a three-spirit. On top of that, I had the maturity to handle conversations about basically anything without a hitch. I could even think through the whole conversation before I had it. If that doesn't strike you as stunning, I don't know what will. That was as a 6th-grader. I still had 3 years until high school. You wanna talk maturity? The average high-schooler's drama? I would rate it a little higher than yours, just from your post. I can see that you aren't very confident about your high school years, and, being skewed because of aging, I'd rate your high school drama just a little more than average. There's my two cents. I hope it helps.

It isnt illegal, the store owner is being a douchebag.  You can print this out and take it over to show him.

Because the store owner is being a weird prick, who probably thinks some ill-advised high-school girl is going to mistakenly stumble in to play.

If he actually called the police, they would get a good and well-deserved laugh out of it, while likely telling him never to call again.

Either insist on your age group thing, or find a different place to play.

well it's not illegal first off, you are allowed to discriminate however you like for your own personal d&d game. the store owner is allowed to set their own rules on who they allow to play in their store however and they could boot you if they wanted to, although they would only be wasting police time if they called them

i would either specify 21+ due to subject matter in your game rather than just no high school kids, or play at home or a friends house rather than in the store

You didn't say where you're from so I can only give examples from the law where I live, here in the UK. Age discrimination is certainly allowed as long as there is a good reason. Obviously no one demands that adults be allowed to play in a sporting league made for children, for example, and even within those teams you'd still expect to put them into age bands. Similarly a company could offer a special trip deal for 'over 60's', and they're allowed to exclude people in their late 50's by saying the trip has been organised with specific facilities and services for older people on the coach. There are many other examples - perks for seniors, limits on financial services, etc, all legal.

So one allowance is "enabling people of particular age groups to enjoy activities together", it might be better to not say 'no high schoolers' ('direct discrimination') but instead state it indirectly, say that 'the purpose of the group is to bring together people of the same age range'.