Some people never have unprotected sex outside of marriage. Others insist on seeing documented proof that there mate does not have HIV or any STDs. The goal for anyone is to find someone that shares their same values and wants the same things that they do.
Very few people will dump someone because they insist on having "safe sex". Everyone is entitled to have their own "deal breakers".
Last but least it's possible they might be insisting on having "safe sex" because THEY have an STD (herpes, genital warts, or something along those lines) and they don't want to risk passing it on to you!
I imagine there are those folks who instead of informing their sexual partners they have HIV, Herpes, or Hepatitis C they'll simply make a rule to never have unprotected sex.