"Morality" has a fundamental problem in that it is arbitrary. Things claimed to be moral in one culture may be disallowed in another. This leads to stupid claims that one culture's morals are better than some other culture's morals, and Historically has even led to war on occasion.
"Abitrary" means that "there is no accounting for taste" in this case.
This is why I prefer to focus on "ethics" instead of "morals". Ethics is not based on arbitrary claims; the concept came along long after morals were well-established.
Ethics can be said to be a study of the consequences of Attempting to Select a Rational Basis for a Society. The Basis may be somewhat arbitrary, but it is not forced on anyone the way morals are. If you don't like a particular Basis, you can go elsewhere and select a different one, and hope others join you.
It should be obvious that if Ethics is to be Universal, then it must select a Basis upon which everyone can agree. This is the best one that I'm aware of:
"People must get along with each other, for a Society to persist in the long long run."
All the Ethics that follows from that Basis must be "in tune" with it. Murder can be denounced simply because it is about people NOT getting along with each other. Ditto with theft and various other commonly-considered-to-be-crimes.
Allowabiltiy of abortion in such a Society depends on the definition of "people", at the very least, but consideration of "get along with each other" is relevant, too. After all, how can you "get along with" a fetus, if you think its actions can be described as "parasitic"? One of the things that people can do, to get along with each other, is "compromise". Every person has selfish desires; this is Known Fact. When conflicting desires meet, compromise is necessary for the people involved to get along with each other.
Well. It happens that a fetus cannot be compromised-with. It will sefishly continue to act in a manner that can be called "parasitic", no matter how much its host pleads for some kind of behavior that is less like theft. Is it any wonder that it is easy to conclude that a fetus does not qualify as a "person"? If it simply cannot do something that persons absolutely must be able to do ("compromise", not "refrain from acting parasitically"), to get along with each other, then why should it be considered to be equal to the persons who can work out compromises, and who thereby are working to help Society persist over the long long run?
In general, no mere animal can be compromised-with. They are incapable of it, although many can be trained in a way that might be interpreted as their saying something like, "Feed me and I'll perform!". This is an illusion, as the training process typically includes both positive and negative reinforcement ("carrot and stick" psychology). Real compromise does not normally include punishments for not accepting the deal.
In conclusion, the evidence is that unborn humans are only animals, and don't need to be treated much differently than the way most other ordinary animals are treated. So, if their actions are considered to be parasitic, they can be exterminated like other parasites. And if their actions are not considered to be parasitic, they can be coddled or ignored or something-in-between. Simple.