In my younger days, I would steer clear of any girl even rumored to have/had an STD. I don't care if she had Chlamydia 3 years ago, it still felt gross to me.
But now that I'm older, having a few STD/I's myself, and educating myself, I no longer think that. As long as the woman is clear of any STI or disease at the time, then I'm ok with it. But you can't just take her word for it, and honestly you have to have your wits about her. No ****ing girls with cold soars, itchy and smelly vaginas, and obviously if you see soars or anything abnormal, run for the hills.
As most have mentioned before, HPV is a lot worse for the woman, and men will never know they have it until warts show up. I had HPV about 4 years ago. I started growing warts on my shaft. I used a home wart freezing treatment, and within a few months they were gone, and I've never had a single wart appear again ever sense.
Like Bible Belt, I also had molluscum contagious for awhile. That **** sucked as well. But it cleared eventually.
Just recently, I caught a UTI from my ex. I've been taking amoxicillin for it, and it's pretty much gone now. But I am still taking antibiotics to make sure it doesn't reappear.
This probably makes it sound like I catch a new STD every week or something... but in reality, this all happened over the course of 4-5 years.
Point being... I've had STI/D's before.. so I am really in no place to judge a woman for it either. In this day in age, you are pretty much bound to catch something eventually. No matter how safe you are. If you are having frequent sex, your risk for catching an STD is great, and only gets greater the more you sleep around.
Woman are not angels. They sleep around, and they are no exception to this rule.
Educate yourself of the various STI's and STD's and it will alleviate a lot of your fear. Most of them are temporary. HERPES and HIV are the ones you really need to watch out for.