In theory and without regard to ethics, yes.

But there are a few major problems.

1. Some STDs are more difficult to test for, accurately, than others. Herpes is a good example. It’s not an easy one to detect and our testing for it is not very accurate. So it’s difficult to tell who we’d need to actually isolate.

2. More of a question of what you mean by isolating? Some STDs can be passed on without direct sexual contact. For example, kissing can spread herpes if someone has an outbreak and doesn’t know it. And because of the inaccuracy of testing, it’s possible for people to have and spread it without knowing. So how far does isolating go? Anyone who’s ever had a sore or blister near their mouth? And are they completely separated from wider society?

3. Stigma is a real thing, and you’d be reinforcing stigmas for very little benefit. Almost all STDs are curable (those that are bacterial infections). Those that aren’t (viral infections) are extremely manageable in today’s medicine. Someone who contracts HIV/AIDS can live a long and full life with good, regular treatment as one example. So there’s no dire/medical reason to separate them from society and reinforce stigma against them and cause psychological harm to them when we can treat every STD pretty well.