The science is clear, U=U (undetectable = untransmittable). HIV, like any other virus, has a cycle. Being HIV+ means that the person is a carrier of the virus, but that does not mean the virus is in the infectious stage of its cycle. In order to infect someone, HIV must be present in body fluids as free viral particles that consist of genetic material encased in a protein capsid that can infect the immune cells of another host. Once it has done so, the virus inserts its genetic material into the infected cell's nucleus, hijacking it to become a factory of more viral particles that will be released into the bloodstream and the cycle repeats itself. When a person's viral load is undetectable, it means that the antiretroviral drugs have successfully blocked the virus replication process. Thus, the virus is still there, inserted in the host's infected cells, but trapped, incapable of transitioning into a new generation of infectious viral particles. In other words, there are no detectable viral particles that can be transmitted to another individual. Catching HIV from an undetectable HIV+ person is impossible.
What's more important here is a matter of trust and your own peace of mind. In many countries it's a criminal offence to lie about your status, but still, I take prep daily just to be sure. Even if he wasn't undetectable —although I refuse to believe that any decent person would lie about that and/or intentionally try to infect someone else—, if you are taking prep regularly (one dose every 24 hours), your chances of getting it are virtually zero. Again, the science is relatively straightforward. HIV is a retrovirus, which means that its genetic material is stored as RNA, as opposed to human cells that use DNA. In order to successfully infect a human cell, a key step for the virus is to transcribe its RNA into DNA to insert itself into the cell's nucleus. To do this, the virus uses an enzime called retrotranscriptase. Prep disables this key viral enzime, and without it, the virus cannot get a foothold in a new host's body, even if it manages to enter an immune cell. This gives time to other immune cells to detect it and destroy it before it gets the chance to hide. If HIV does not successfully insert itself within ~42 hours, it's game over for it.
So my advice to you is, firstly, try to rationalise fear. HIV is far from being a death sentence as it was decades ago. Secondly, don't make it a case that you wouldn't want this person for that reason. I imagine they have gone through their own process of acceptance of their new reality and learned to live with it. These days, HIV+ people can have normal lives. There's no reason to discriminate. And lastly, for your own health and peace of mind, get on prep, test regularly for other STIs and enjoy sex with or without condoms which make little difference these days.
