How many sexual characteristics are actually necessary or useful in a modern society in which sex is no longer a means of procreation?
Very few, in my opinion.
I know that sex has purposes beyond reproduction... or, more (likely) more accurately sex has results that will increase the likelihood of 1) having sex again 2) production of a child.
The part that I am most familiar with as being useful outside of reproduction is "post-coital bliss," where hormones are released that makes one feel happy/content and de-stressed.
Therefore, should post-reproduction era humans retain some sort of facsimile to sex? Yes.
But does that mean that all of the associated organs are still needed? No. Breasts, although very pleasant, already have seen much of their function eliminated in modern society.
More children are bottle fed than breast-fed (or breast-fed and bottle fed), which means that the female breast has become largely an object for sexual attraction.
Why do I like breasts? Is it because they are useful for me, or are they useful for feeding babies?
Moving on, if our new society had a replacement for the uterus, an artificial uterus, uterine cancer can effectively be eliminated. If ovum can be artificially duplicated ovaries can be eliminated, etc, until one is left with whatever it is that defines a human being.
How many (sexual characteristics) are actually detrimental (are susceptible to disease, distract from rational decision making)? What's the easiest way to deal with detrimental sexual characteristics?
I'm afraid I don't have an answer from this outside of what I've already posted
And, does elimination of any these harm a society?
I think not, as a society may be considered to be equivalent to an ecology, which can generally survive or thrive with the elimination of certain species. Do our modern ecologies rely on the mammoth, dinosaurs, etc? Obviously not.
Therefore, I feel that the male sex is an unnecessary part of the future. I am aware that two females are currently capable of reproducing, although I'm not certain if a sperm surrogate for one of the pair's members is necessary for carrying the genes of that member with current technology. Also, children born from a two-female union are always female, thanks to the way male-female chromosomes pair.
I'd like to think that the resultant society would be closer to some sort of utopia, with greater equality etc. etc. but I don't trust human nature any further than I can throw it.