How much weight is safe to hang from a 1/2 inch thick maple board mounted to the wall?
I would use a T-nut on the back. If you are using softwood, you can usually pull the nut flush by tightening hard. With hardwood this probably won't work, instead, counterbore with a Forstner bit just enough so the nut is flush. With this method, the wood will be almost full thickness and you can re-tighten from the front if necessary.
The T-Nuts that you are likely to find at a home improvement store are designed for softwood. They might work, but there are special T-nuts for hardwood.
https://www.mcmaster.com/tee-nuts/
IMO, a T-nut and hardwood will be really strong, the weakest point will be the lag bolt pull-out strength. I would use 4 lag bolts. The top two are the most important. You want the top two lags into the stud to be near the top of the board. If the distance between the barbell downward force to the pivot point is larger than the distance between the top lag and the pivot point the force will be amplified.
There are tables to determine lag-bolt pull-out strength. You need to account for the moment arm (distance to the pivot point). If the distances are about the same, then the force on the lag-bolt will be about the same. It is difficult to tell from the pictures, but the distances look to be similar.
Be sure to account for dynamic loading, don't assume that people will always gently put the barbell on the holder. I would use 3X, so you want to support about 450 lbs momentarily.
I am having trouble finding a definitive website, but I believe that a 1/4 lag screwed into a wall stud has a pull-out of about 300 lbs. So, the top 2 lags should hold, assuming that your moment arms are about equal.

Edit: since Forstner bits are something you may not have or want to buy, you could use a spade bit for the counterbore, the hole won't be pretty, but it won't show.