Campground smoke in your rv

Wear one of these if you can't handle the smoke:https://www.amazon.com/Respir%D0%B0tor-Reusable-Compatible-Protection-Polishing/dp/B08MW3NPZV/ref=sr_1_1_sspa?crid=3VCLVH2X4ETMN&keywords=gas+mask&qid=1649000839&sprefix=gas+mask%2Caps%2C1132&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExNVZJSUZGVDUyUUxFJmVuY3J5cHRlZElkPUEwMTYyOTA3MzVQN0NZQVVZOTlGVCZlbmNyeXB0ZWRBZElkPUExMDE2MjI0MkpKWjc1WjJBQ05QTyZ3aWRnZXROYW1lPXNwX2F0ZiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU=

Leave or never go there to begin with.

But you can have the opposite effect with fans blowing into the camper from the opposite side ( or ac) . This will build up positive pressure in the camper and may limit smoke intake. So there is that. Unfortunately, with wood restrictions , you get some wood that is less then ideal to burn. That leads to smoke. One of the reasons I got a propane firepit. I will burn wood if I can and its good but usally its not seasoned wood and dosen't burn well. Its not always the campers fault.

Would a desktop electronic air purifier do any good? I know it kills bacteria but wonder if it has any effect on smoke particles which are unhealthy to breathe.

When campfires are allowed, tolerating it or moving are about the only choices. Running an exhaust fan will likely only make it worse. For all the air that the fan exhausts, there has to be incoming air to replace it. And that incoming air will be smoky. And if the wind is blowing smoke toward your RV, a box fan is not going to do much.

Bring a small box fan, point it at the offending camp fire and leave it running as long as the fire is burning. Smoke contains several known carcinogens. Some people throw items such as plastic wrapping into the fire which makes it even more unwanted.

Building a fire with minimal smoke is a lost art. Yes I would do my best to tolerate the smoke.
If there are special sensitivities to the smoke it is probably be to choose the campground accordingly.

It seems to me you are in the wrong place. When at the rodeo it will have a certain atmosphere. If that's a problem the choices are few and obvious.

The smoke issue is the one of reasons why I rarely stay in developed campgrounds - private or public. Noise is another. Consider becoming more able to boondock with all the comforts.

Fortunately, I don't camp where sites are so close together that smoke from a neighbor's campfire fills up the inside of my RV.

I'd say you have two options:

Choose campgrounds that are more spread out (eg, national forest campgrounds); or

Use your RV exhaust fans. Turn them on BEFORE the smoke becomes a problem and leave them on until the campfire is put out for the night.

If neith of those solutions resolves the problem, then you may be overly sensitive to smoke. In that case, you may be limited on options.