However, there are also people that will never really attempt to understand, so these things will persist.
Yep, I think that is an [unfortunately] important part of the public policy issue.
As to the utility argument, I find the logic leads to unintended consequences. The black market, back alley abortion disaster argument is usually exaggerated. Numbers were thrown out there that up to 15,000 women a year died before Roe v. Wade, but data from the US Bureau of Vital Statistics and the National Center for Health Statistics dispute that claim putting the number between 30 and 50. There is also the argument that women make the choice to have black market abortion, and thus have weighed the consequences and determined the risk is worth it. To alleviate some of the risk by legalizing and regulating abortions (which are not always as regulated and sanitary as people think) creates some logical consequences. Why not legalize and lessen the risks of other activities? Why does this logic apply only to abortion? This argument is also used as a basis to provide free/taxpayer abortions because excessive costs can lead to the same black market…but again the same questions apply, why not provide this for other things too?
At the end of the day, the utility argument is about costs vs. benefits (and not just financial).
On the black market- the lower numbers may well be true, but it all depends on the actual studies and the methodologies. It is those that need to be evaluated. As for those who still get black market abortions- of course they weigh the risk, but the risk is still a lot higher than had they been able to do it in a legal establishment.
As for legalizing and reducing risk of other activities- again it comes down to costs and benefits and should be evaluated as such. Things like marijuana, I would argue, should be legalized.
But the black market isn't my only argument in that debate, it is just an example I gave (same with quality of life). Things like impact on crime also play a role (there are studies that suggest legalized abortion is primarily responsible for large drops in crimes in metropolitan cities like NYC - the book Superfreakonomics [or perhaps it was Freakonomics] popularized that one. All of these things should be considered.
And the question of taxpayer funded abortion is again all about costs and benefits. From what I have read, I am inclined to say it is a bad idea (although private charity provided abortion is a whole other thing), but I haven't done nearly enough research into the matter to give even a semi-confident opinion. Yes, a black market can form if costs aren't low enough, but that is the case for anything- that happens with cigarettes too- it doesn't mean we shouldn't still tax them heavily. Again, it is about costs and benefits (not trying to sound like a broken record

).
The problem with utilitarianism is often that it is hard to effectively measure all costs and benefits, but I think in many cases we can still make smarter decisions considering what we can measure with the methodologies we have at hand.
The quality of life argument is highly subjective and has some definite logical consequences. Are those who live lower quality lives less human? Do they have a right to live and drain resources from society? Do they have less right to pursue life, liberty, and happiness? Do life circumstances determine potential contribution to society? Who determines what “quality” in life means? Typically the quality of life arguments relate to the poor, yet people would never use these arguments about poverty in any other context than abortion. In fact, many of the people (obviously not all) who use this argument are the same people who vilify wealth and extol the virtues of poverty.
Just because we don't have perfect measures, does not mean we cannot take facts-based action that improves circumstances. This happens all the time in healthcare, even though the US generally hates to admit it. When it comes to end-of-life decisions, this is very often the case. The US due to its culture does have a bigger issue with it, which is one of the reasons why I think we try to extend lives so much and at such great costs compared to other nations.
Also, making human rights decisions or laws based on social utility sets the base argument for socialism. If everything was measured by the benefit/gain to society then many freedoms we recognize today would not exist; our actions would be controlled by what is considered best for the collective. In a free society people are allowed to live as they see fit and hold responsibility for their choices. However, in an engineered society people are guided by laws for the “greater good” (a subjective phrase), and consequences are forced upon them. While the abortion argument is often phrased as “reproductive freedom,” the utility argument has the logical consequences of lesser overall freedom.
I disagree that it is the basis of socialism because maximum utility, especially over generations can very arguably come from a relatively free society. And historically, some of the most famous utilitarians such as J.S. Mill have in fact been very "pro-liberty" and for individual rights. A more contemporary example is Milton Friedman, who often argued on utilitarian points and was of course a big proponent of capitalism. I am not a philosophy or history expert by any means, but from my readings I think there has historically been a greater link between those advocating libertarianism and utilitarianism than those advocating egalitarianism and utilitarianism.