> Global mandatory inoculations using a safe and effective HIV vaccine that causes false-positive results on HIV tests would be a field day for anti-vaxxers and conspiracy theorists everywhere.

There's no reason for it to be mandatory. It's not like COVID19 or the flu where it is often transmitted through casual contact. There is simply no reason to delay/halt an HIV vaccine for just causing an false positive on a test. As you said, any effective HIV vaccine will likely have this issue so pushing forward is the only option.