Do you care about your significant other's sexual past?

[Pyrrho]

... But something dawned on me, which was the idea that if they cheated on me, I wouldn't care, as long as it was safe, and no diseases were transmitted.

The thing is, nothing is 100% safe except abstinence.  Even if she only has sex with others with a condom, there is a chance she will contract an STD.  And, she is not going to immediately know if she has a disease or not, even if she is careful to be regularly checked for diseases, so you will have no guarantees of safety from any STD.  So, monogamy is safer than promiscuity.  (That, of course, does not mean that one must or should choose monogamy, but it is something to keep in mind when deciding about such things.)

At first I thought this was a reflection of how little I really cared for that person, how bonded I was, and I subsequently broke it off with many of them, but now I just think its an extension of having realistic expectations and ideals of what love means.

Neither my wife nor I have any difficulty with monogamy.  My wife and I have been married for over 20 years, and are still very happy with each other.  We expect to be happy together until one of us dies.  The fact that some people do not stick to one person has no bearing on the question of whether others find it difficult or not.

If other people wish to be promiscuous, that is not a problem for me.  I wouldn't marry such a person (or become lovers with such a person), because that is not what I want.  This compares with people being incompatible for other things, like one wants to live in a city, and the other in a forest.  Those people cannot be together and both have what they want.  There are many things like that, that make people incompatible, which does not necessarily involve a moral judgement, or a judgement about anyone's intelligence, or any other such thing.  People often have different, and incompatible, preferences.

I'm still not confident that this is the right way to go about things, so I thought I'd air it out. If a woman was honest with me and wanted to have other sexual partners, I'd say go for it and get tested. Am I wrong in viewing this as an extension of being at peace with your partners past?
...

I agree that it is conceptually an extension of being at peace with your partner's past.  It all depends on how one views sex, and how one feels about it.

Many people seem confused about this point, so I will state it explicitly.  Feelings are fundamentally not rational.  If you like chocolate,  and someone else likes vanilla, it isn't a difference of reasoning that separates the two.

So, if someone wants sexual fidelity, and someone else doesn't, the difference in feelings is just a difference in feelings.  Usually, the discussion of STDs is a rationalization for one's feelings that are not based on that at all.  I personally want monogamy, and expect it of my wife, which was our agreement in the beginning (which is when you need to make your agreements on such things).  I could pretend that it all had to do with STDs and, in the event of pregnancy, knowing who the father is, but it really isn't based on those things, though they do encourage me to not try to change my feelings on the subject.  It is a matter of what I want, and what my wife wants.  We also want to listen to Mozart occasionally, and so we do.  If you don't want to listen to Mozart, you don't have to.  (Of course, everyone should love Mozart!)

I suppose I might as well add, sometimes people do not really know what they want, and pretend that they don't care about things that they do care about.  I remember discussing some of this with someone who said he wanted open relationships, because he wanted to have sex with multiple women, and did not care if his girlfriends had sex with other people or not.  The thing is, when one of them told him about having sex with another guy, he did not like it.  He was basically okay with it as long as he did not know about it, which, of course, means he really did care (otherwise, the knowledge of it would not bother him).  My guess is that he thought he ought not care, because he could not think of a reason to care.  But feelings are fundamentally not based on reason.

Reason has nothing to do with ultimate goals; it is useful in determining intermediate goals, as reason is useful in determining means to ends.  But ultimate goals are a matter of feeling.  David Hume expressed this idea thusly: 

"Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them."

http://oll.libertyfund.org/titles/342#Hume_0213_877

And:

"Reason being cool and disengaged, is no motive to action, and directs only the impulse received from appetite or inclination, by showing us the means of attaining happiness or avoiding misery: Taste, as it gives pleasure or pain, and thereby constitutes happiness or misery, becomes a motive to action, and is the first spring or impulse to desire and volition."

http://oll.libertyfund.org/titles/341#Hume_0222_603