The second sexual revolution.
For purposes of a more compelling answer than "What would happen? Well, basically whatever is happening now, because you've described something only slightly better than today's level of technology", I'm going to assume the following important things:
1. "immediately indicate" means that the test will successfully pick up an infection with effectively zero incubation period (say, within a matter of hours after intercourse)
2. 100% sensitivity and specificity (all infections are identified, with no false positives)
3. as with existing cheap & instant HIV and pregnancy tests, the comprehensive test is available for home use (can be self-administered, as <PERSON> pointed out)
Conditions two & three are definitely important, but I feel that number one is key. This, combined with the comprehensiveness of the test, would provide ironclad assurance that a potential sexual partner was not a health risk.
The Achilles' heel of the current generation of STI tests is that they are based on antibody response -- which is variable, and takes too long. 225
This is a nuisance for the responsible, and the root of the sexual health threat posed by those who are not. With an instant test, waiting for incubation periods to pass, and indeed, waiting for test results at all, would become a thing of the past.
The stigmatization of premarital sex took a heavy hit when contraception and abortion became widely available. The stigma of multiple sexual partners being a health safety concern will likewise come under fire, as the threshold of effort and self-control required to be cautious with one's personal sexual health would be drastically lowered.
It would become socially expected to test oneself in the presence of a new sexual partner prior to intercourse, as a gesture of openness and respect. Refusing would be like not buckling your seat belt in a car -- what possible excuse could you have? It is to be hoped that it could even be packaged directly with traditional forms of contraception.
Additionally, we have two things now widely available that the first sexual revolution did not: social networking and location-aware communication devices. It would be short work to adapt already-existing dating apps for more overt purposes. This creates the potential for unintended and possibly unsettling consequences, like the network-wide "blackballing" of STI-positive individuals. 998