A person going in to have an abortion would indicate that she has a fetus of another person inside of her.
First, that is operating under the assumption that she did in fact go to a doctor to have the procedure done in the first place.
Second, you're requiring EVERY woman's Doctor to violate Doctor Patient Privilege by making her pregnancy a matter of public record upon discovery. Even the doctors of women who DON'T want abortions.
Third, the results of the second problem will cause significantly more of the first.
As history has shown us that when you attempt to ban abortions you do not actually prevent abortions you simply cause women to perform self abortions or obtain black market abortions which increase risks to the mothers health. Just like Drugs, Alcohol, and Guns attempts at banning them are utterly futile and generally cause more problems than they solve.
With your logic, the 4th amendment would allow a slave owner to continue to have slaves as long as they remain on his property.
No, it would allow a slave owner to continue to have slaves so long as he can keep them hidden from view of the outside world, and prevent authorities from having probable cause for thinking he had slaves. Police cannot simply go around searching random property in the off chance that you might be hiding slaves, drugs, prostitutes..... They need some probable cause or evidence that would allow them to get a warrant. With a pregnant woman there is no such probable cause or evidence that would exist until significantly into the pregnancy. Furthermore even if a pregnancy was known there are a plethora of valid reasons why a pregnancy could go badly that are not the fault of the mother in anyway. Attempting to judge which women had intentional miscarriages would undoubtedly result in horrifying results. Identifying whether you have slaves or simply African American guests is easy. You can just ask them if they're being held against their will.
It would be nice if everyone had the humility to understand that they could possibly be incorrect.
That starts with people like yourself.
You really don't think that people should be allowed to do business with businesses that they like?
You are always welcome to choose which businesses you buy products from. Why you like one person's services as compared to another is entirely your opinion and it is impossible to determine what motives you might have. However when you are selling a product you cannot choose who you sell it to unless their actions during the sale differentiate them in some way. If the product does not change from one customer to the next, and the reimbursement does not change from one customer to the next, and the actions of the customer while in your present do not change, then the only motivation left is that you have a disdain for the person. If you have no personal affiliation with that person(ie they are an ex-wife) then bigotry is all that remains and it is very easy to determine that and prove it in a court of law.
The key to both the Abortion problem and the bigoted business problem is whether or not it would be reasonably possible to determine if a crime has been committed without requiring the individual to incriminate themselves. If there's no method of reasonably doing that then there is no way to enforce such a law. With a cake baker it is very easy to deduce the motivations of the baker. However with a customer it is virtually impossible to determine why they might choose to shop at one business or another. Even if someone chooses not to shop at a Jewish super market due to the fact that they are anti-semetic there's a million excuses they could use for why they want to shop at a different store all of which are valid. With a woman, it would be virtually impossible to know if she had an abortion or a miscarriage or in most cases whether she was even pregnant in the first place. Therefore you cannot reasonably prevent abortions. All you can do is impose massive harm to all women every where. Even the ones not having abortions.