With travel, I understand that there is a higher risk of lots of diseases, and testing against all possible infectious diseases is not feasible. Drug use is also obviously disqualifying. But why would you care about someone's sexual behavior? The blood must be tested for common drugs and common blood borne diseases regardless, and it's perfectly possible to engage in sexually risky behaviors and not have any venereal disease (unlike with drug use, where it implicitly means you will have levels of those drugs in your blood), just like it's possible to be very careful with your sexual behavior and still get a disease.
Note: for tattoos, I have no idea if the problem is also related to venereal diseases, or if there is any problem from contamination with the tattoo ink itself, and I don't care enough about this subject to look it up.
The answer to all of that is mainly hepatitis C, that can have a window detection of 6 months, even more.
And yes, you can be very careful and get a disease. But they are playing statistics here: over 60% of injected drug users have Hep-C, that means a lot of prostitutes. They won't and shouldn't trust anyone who say "hey, I had unsafe sex against all advice, but was very careful with the tattoo in a dark cellar and the heroin party, pinky promise".
Unfortunately tests are not 100% accurate and there's a window between when the pathogen is present and when it's detectible. Add in that many viruses aren't directly detectable, the tests look for antibodies to the virus.
This is why they usually ask if you've had a new sexual partner in the past 3 or 4 months. This is the window period for detecting some STDs and other diseases.
For tattoos, if the artist isn't using a brand new set of needles for you, you risk bloodborne disease transmission, with hepatitis B being a particular danger.
> But why would you care about someone's sexual behavior? The blood must be tested for common drugs and common blood borne diseases regardless, and it's perfectly possible to engage in sexually risky behaviors and not have any venereal disease
Men who have sex with men are something like 50-100x more likely than the general population to acquire HIV. HIV tests do not have a 0% false positive. They will not catch all very recent infections. The rationale for excluding them until recently is that it’s defense in depth and it doesn’t hurt the blood supply much because they only make up about 2-3% of the population.
The current rule is that MSM don’t face a blanket ban, but if you’ve had anal sex in the last 3 months you have to wait because anal sex is inherently more likely to transmit HIV and the tests may not catch a very new infection. Other diseases like Hepatitis have a similar issue.