If they told me upfront than no. There is absolutely no reason for me to risk my sexual, physical, and emotional health for someone who may not last. If this is a new relationship and even if I feel those pangs of "this could be going somewhere", there is absolutely NO reason to pursue any sort of sexual activities.
If they tell me they have herpes or gonorrhea than what else could they have that they wouldn't be so willing to tell me? If it was a treatable disease than why haven't they treated it yet? And how soon was their last sexual partner from me if they still have it? I have no interest in being with someone that sleeps around or doesn't use protection with their partners- it says to me, if they're so careless with their own health and safety, how will they be with my health and safety?
In a world full of uncertainty people need to take their sexual health seriously, if it's a partner that didn't know they had it because they weren't tested than I don't want to be with them. If they can't be bothered to be regularly tested than that's not the type of partner I want, I do not want someone who hops from bed to bed with little regard for themselves or their partners.
This is all rhetorics and being married it doesn't' really apply to me. However, if the time were to come where I wasn't with DH, I'd still take this seriously. I have PCOS which already puts me at a higher risk of endometrial and cervical cancer, I'm not going to further put myself at risk of HPV or various STI's- it would be a new chapter in my life, why ruin it with something that has the potential to last a lifetime?
My body is a temple, yes, I occasionally destroy it with fast food even though I know the dangers... but to risk a lifetime of either infertility, depression, cervical cancer, or pelvic pain caused by any various STI is not worth the risk.