Condoms don't eliminate the chance of contracting an STD.
They do, however, greatly reduce it, along with the odds of an unwanted pregnancy.
While abstinence and celibacy are the only surefire ways to prevent either, is it your wish that those who DO engage in sex, do so without any ability to protect themselves at all? Do you sincerely want them punished with disease and/or a pregnancy that they can't afford?
Keep in mind:
(1) the sex drive is one of the strongest, if not THE strongest, instinct, that humans possess;
(2) Abstinence-only sex-ed hasn't been shown to significantly reduce the rate of STD infection, because students of such have a tendency to engage in risky sexual practices short of full intercourse without protection;
(3) Someone infected with an STD may infect multiple partners before they're diagnosed and treated;
(4) the state may wind up footing the bill if the person cannot afford to pay for diagnosis and treatment, which may translate into many millions of dollars per year lost to illness;
(5) unwanted pregnancies directly translate to an increased rate of abortions;
(6) if carried to term, mothers or couples with illegitimate children may be forced to seek welfare assistance to help raise their unplanned child, which also costs the state money.