Anecdotally every poly person I know is (relatively speaking) quite diligent about STDs, getting tested way more than most, informing partners etc etc. Sometimes it seems to me like poly is actually a spreadsheet fetish with relationships on the side.
I think polyamory is more threatening to "traditional" values due to emotional risk / complexity and impact on family structure, parenting etc. One of the gnarlier problems is wealth transmission.
In many countries you are de facto with someone after just 2 or 3 years, this is already crazy, you get in a relationship with someone and a few years later you owe them half your house. Bring poly into the mix and if you a) have assets and b) cohabit then things can get messy real fast.
Very basic stuff like welfare and taxes haven't really caught up with this either yet, practical things like what do you put in the "partner's income" box on many government forms. The bureaucracy is really not set up for this.
That said: It's important to know your status, even if you're monogamous.
People in poly relationships tend to know their status better than monogamous cohorts. Thus, even if one partner has an incurable STI, they're usually aware that they have it, and keep their viral load undetectable (which prevents transmission), so the factors round the risk down to the same very low range, despite more people involved.