It really depends on the STD.

A lot of polys and swingers I've met have accepted herpes and warts as par for the course. Some disclose, some don't. Good to keep this in mind and ask partners about their std history. I've even gone so far as to request documentation from their last std screen.

There are HIV positive folks who seek out other HIV positive folks to have sex with. It's been found that the dreaded HIV superinfection never happens, so these folks can bareback together without worrying about infecting someone else with HIV. There are HIV tests now that can give results in under 20 minutes, and they are available to the private consumer online, if you really want to know a potential partner's HIV status.

Other infections like gonnhorea, syphillis, etc. are more treatable with anitbiotics. But it's still no party if you get infected with one! So again, requesting recent std test results is quite common in certain circles. And so is condom use.

People often don't even know that they are infected with something, it's quite possible they don't have symptoms, and then of course some people lie. My view is that it's better to err on the side of caution and use condoms. Even then, a visual inspection of genital areas is a good idea, because condoms don't fully protect against herpes, warts, and a few other things. The more partners you have, the more likely you are to have these things, so it's that much more important to take precautions in poly life.