Communicable diseases are of special interest to all the citizens of a Republic. Whether you have nothing, or are among the wealthiest people in the world, you have an interest in the detection and treatment of communicable diseases in the people around you.
In New York City in the first decade of the last century, Typhoid Mary infected more than 50 people that she came in contact with as a cook. Poorer people generally both fill the service roles that wealthier people use, and, it can be imagined, are less willing to visit a doctor if they suspect they might be ill. This is because they can't afford it, and they can't afford to lose their wages if they are sick and their illness forces them to be quarantined for any length of time.
It is self-interest that none of are infected by the people around us, and we don't even care if the person doing the infecting is here in this country without documentation.
It might be an issue whether or not STDs are covered. That all STDs can be transmitted through other means suggests that they should be. In addition, for good or ill, it is clear that most people share some risk. Ironically, recent history has found some of the loudest critics of this state of affairs engaging in the behavior which puts us all at risk.
As a general rule, it is also in all of our interests to be treated for communicable diseases. People with health insurance mostly are already.