First, let me say that I don't believe there is a "one size fits all" way of dealing with all relationships, and that people need to know their mates and go from there. But regarding STD's and such, I feel that sexual responsibility is on each us, as individuals, and we have to do whatever we can on our end to lessen risks. If that means, as a woman -- even a married woman -- that she requires the use of condoms, it's her right. Just as it's her husbands right to not be okay with her decision.
Personally, I think it's unwise to have 100% blind trust in anyone. We're raised to "be aware" of this, that, and the other all our lives, but toss all of that out the window JUST because of marriage. Not me.
And I'm cool with being asked for a paternity test because I don't roll like that. I am also person who likes to be sure about things/situations, and wouldn't blame my husband for being that same way.