When chalk painting dining room chairs would just waxing be okay?

http://www.diybeautify.com/2017/01/top-coat-protection-options-for-chalky-painted-furniture.html

I'd be worried the wax would rub off on someone's clothes.

I think you have to redo the wax every several years (some say even every several months), which is why people don't do it often, and use a regular water based poly or clear sealer instead. Here is a link one blogger wrote about the cons of waxing:

http://paintedvintage.com/to-wax-or-not-to-wax/

Assuming you use microcrystalline wax, it should penetrate the chalk paint and won't rub off on clothing, but the advantage of polycrylic is that it's much more durable, and you won't have to re-apply it regularly. Here's a blog post from someone who's done a lot of painted furniture: https://teamhealthymom.com/single-post/polyurethane-chalk-paint-what-i-wish-id-known/

clear coat

I chalk painted my desk which gets daily use and finished it with wax. I didn't want the look of clear coat, even the matte finish. I used a couple layers of wax, buffing with a cloth extremely well after each coat. That was 2 years ago and the paint job and wax finish have yet to chip!

i have been doing DYI ing for 43 years before there were all these products. I don't listen to anyone for the most part. Wax attracts dust. Try going without doing anything. I have a collection of all types and shapes of stools one I painted the rest were already white. It's fine it's probably 20 yrs old gets used sparingly with zero problem. Trust your own judgement! You can always do something later but to clear coat them all, too much work for me! I've made my own milk paint and I stick with that when painting anything. Have not tried chalk paint but, pretty sure it's a tad bit like milk paint just open a jar or can and viola. The only other product I've used over milk paint is linseed oil.