Absolutely. All service members must be deployable to an arena of conflict, and someone with infectious blood is just a landmine waiting to hurt someone. And if their supply of drugs to ward off an infection flare-up is cut off, they become AIDS patients, with all the drag on resources that that entails.
The access to medication puts them on "nicer" deployments which is unfair to other military members who then get sent through the sandbox repeatedly.
It also means high risk for them if they were to be captured in battle. In addition, the U.S. would be forced to negotiate for their release at a severely disproportionate political disadvantage.