Usually yes, but state vehicle (and trailer) tax laws vary a lot so do some research on your specific situation.
Typically taxes are paid when registering/titling the vehicle. There are a few ways to avoid double taxation, and usually at least one of them will be available to you:
1. Do the paperwork necessary to get a registration in your home state before going to pick up the trailer. That generally will require some degree of cooperation from the seller (and mutual trust) to exchange money, bill of sale, etc. via mail or fax or whatever.
2. Many states will offer a temporary registration or transit permit for a nominal fee that allows an out-of-state driver to drive or tow the vehicle to their home state. This is often the easiest approach. Generally you don't need to pay sales tax for these permits; if you do, many states will offset the sales and use tax you need to pay when you actually register the vehicle. Some states also offer these sorts of permits for bringing in vehicles you purchase out of state.
3. For a popup especially, you could fairly easily put it on another trailer or in a box truck or similar to bring it home. Obviously it does not need to be registered etc. when it's merely cargo.
