I don't know you or your religious beliefs, but many people who believe that 'life begins at conception' arrive at that belief through their faith. I would ask that you examine your heart for empathy, and see if your beliefs are consistent with your values, especially when it comes to the power given to the state.
It also seems that you are willing to cut the power of the state very very fine - intentional killing of a fertilized egg is equivalent to killing an infant, but the state does not have a catalog or any way of knowing about all fertilized eggs, so how does it know when to investigate?
The state has no right to know about a woman's IUD, but does have a right to know if she has taken steps to stop that fertilized egg from developing further, if I understand your position correctly.
We get our belief system from our family and friends. We see their values and we see what works for them. We feel righteous when we defend those values. This is true for everyone. It's not "both sides" it's "all humans".
I personally view humankind as my cousins. I don't like all my cousins, I don't agree with everything they do. Some need help, some need to be stopped by force, some are greedy, some are kind. If we're all cousins, then we all have rights, and we have to decide how to balance those rights. A pregnant woman has rights, and an unborn child has rights, and those do need to be balanced. I am comfortable putting the balancing point at some measure of 'viability'. I am not a specialist in pregnancy, so I don't know exactly when that is, but it's definitely not at the moment of conception.
> the state does not have a catalog or any way of knowing about all fertilized eggs, so how does it know when to investigate?
> The state has no right to know about a woman's IUD, but does have a right to know if she has taken steps to stop that fertilized egg from developing further, if I understand your position correctly.
The state can make something illegal without needing intrusive investigative powers to be able to find it. Consider that CSAM is illegal, even though we don't have a national registry of cameras or hard drives, and the government isn't allowed to search your cameras or hard drives for CSAM without probable cause.
Isn't that true of most other reasons that people go to hospitals too? Why should this one in particular be free?
> If a bully breaks your kid's arm, should their family pay the doctor bills?
Isn't the way this works that you'd have to pay the bill initially, and then later be able to go after them for compensation?
> If your date takes you to a restaurant you don't want to go to, should you have to pay the bill?
Can't you just decline to go to that particular restaurant?
> And if the baby is not adopted?
Then the baby would end up in the foster care system. Not a good outcome, but a way less bad one than being killed.