Analyzing this from a rational (libertarian) perspective...
First, regarding abortion and the right to choose. The right to choose would most likely not be restricted, but rather expanded to include the option of removing the foetus from the mother's women and placing it in an artificial womb. Questions formerly irrelevant under libertarianism, such as whether or not the foetus is a "person", may become relevant. When abortion or birth are the only options, whether or not the foetus is a "person" is irrelevant; no-one has the right to invade the property of another, least of all one's body, and everyone has the right to take whatever action is necessary to remove unwanted individuals from one's property. If you are tresspassing on my property to obtain shelter, I can throw you out, without myself being obligated to pay for your shelter. The same logic would apply to a pregnant woman. However, one thing that would change is that, if we determine that the foetus is a person, measures be taken to make sure it survives expulsion from the uterus, if possible; however, the woman would not be forced to pay for incubating it in an artificial uterus. Christians could pay for that with their own money if they so chose.
Now, regarding some of your concerns:
If artificial wombs provide safer environments than natural ones, it might be possible for pregnant women to be forced by the courts to have their fetuses placed in artificial wombs instead. In the case of a crack addict mother, this is probably not a bad thing, but given the nature of our court system, a social worker could see a pregnant woman wearing a seat belt improperly or performing a risky activity, and have the fetus removed from her for its own good.
Nope, this would constitute the initiation of violence against the woman. No-one has the right to cut open a woman's body because s/he thinks the woman isn't a fit mother.
Combine artificial wombs with cloning technology and a donor egg, and gay males can actually have their own biological children. While many people would see this as something amazing and wonderful, right wing conservatives and the ultra-religious would become apoplectic.
Who cares what the religious right thinks. It isn't their children. If they don't like homosexuals, fine; doesn't give them the right to prevent homosexuals from having children.
Health insurance companies might encourage or even require that pregnancies occur this way, simply because it would be cheaper for them in the long run.
Well, that's up to them to do or not to. If women don't want to do that, they can find a health company which doesn't require it, or pay a higher premium. For a clear description of how insurance works, and why it's not wrong for insurance companies to request such things or (if not) require a higher premium, see The Insurance Scam.
Companies might attempt to write clauses into employment contracts stating that if a pregnancy interferes with work, then the fetus must be transferred into an artificial womb. While the average fast food clerk, secretary or computer programmer might not have to worry about that, female executives or laborers would.
Well, the woman could always choose to void such contract by not doing so, in which case the company could fire her. If she doesn't like that term, she can look for a company that doesn't require such a thing. Companies that have such dubious requirements are not likely to attract many talented women.
Would mothers feel less attached to babies to whom they did not give birth to?
Depends on the mother. There are millions of adoptive parents who feel very close to their children, despite the fact that they didn't give birth to them.
It would be easier for researchers to harvest fetal tissue for research, giving rise to numerous ethical and legal issues.
Ethical questions can be dealt with by norms and boycotts. If religious people don't like the ethics of fetal tissue research, they can refuse to do business with those who do such, refuse to let them into their churches, and otherwise boycott them and exclude them by norms. Those who don't have any problem with such won't do that.
Could this lead to eugenics?
Eugenics most likely would require gene therapy and genetic engineering, which is also possible in the future. Artificial wombs are not necessary for eugenics, nor do they encourage it. In regards to eugenics, gene therapy and genetic engineering is a choice for every parent to make. Again, those who don't like it can deal with it by norms and boycotts. In no way does it constitute the initiation of violence against anyone else.
How do the major world religions feel about it?
Who cares what the "major world religions" think? If we halted social progress every time they got their panties in a bunch, we'd still be thinking the sun revolves around the earth, we'd all be getting from place to place on horse and buggy, women would still be wearing chastity belts, and we'd all think sex was an evil horrible thing.
Would their be any complications or developmental issues for the fetus before or after birth due to things that might be missing from an artificial womb, such as maternal heartbeat, hormones generated by mood, touch, etc.
The same questions could be made of for incubators for premies. In short, simply because we don't know all of the possible negative consequences doesn't mean we shouldn't proceed. Certainly, the solution to any possible problems is not for government to step in, but to let the free market work unhampered.
Social Security is a pyramid scam.