For me, I insist on talking to the other person's partner before I will invest any time into the relationship. For me it's about openness and honesty and I expect that of any person I am with.
I haven't been like that in the past, have been willing to "bend" on this type of issue and it has pretty universally ended in grief of some sort. I don't have time for that in my life.
Part of what I need in my relationships is trust. If they can't be completely honest with their partner, someone that they supposedly have a committed relationship with, then how can I expect them to be honest with me about issues vital to me like sexual history/STD testing and the like?
It may work well for others, I know, but I can't, or am not willing to do it.
"Listen, or your tongue will make you deaf." - Native American Proverb