No conflict. One can choose to not be a parent by not copulating.
On the topic of abortion, you have a problem of conflicting rights: the right to choose to be a parent vs the right to life.
I find it hard to conceive of any situation in which the right to choose should supercede the right to life.
Abortion advocates often justify their position by dehumanizing the victim, thus negating the right to life. But dehumanizing the victim puts you on the same moral footing as Heinrich Himmler. I don't think it's a valid position.
https://www.reuters.com/legal/idaho-asks-us-supreme-court-allow-near-total-abortion-ban-2023-11-27/
Discussion
I think the Roman catholics are right about not separating sex *for companionship and pleasure* from *sex for procreation*
The latter is the organic consequence - the fruit - of the former
What God has joined together let no man separate asunder
If sex leads to fruit then thise who caused the child to be have a duty of care for that child. Can't escape nature. I forgot which libertarian had an excellent case for this based on common law and tenancy etc.
I have an analogy I use sometimes.
Imagine you're walking down a sidewalk and somebody throws me off a building and I land on you. You are injured, but you also broke my fall and saved my life, for which I am grateful. Now who should be punished for your injury, me, or the person who threw me off the building?
That is an analogy for non-consensual procreation. The person who threw me off the building should be punished for what happened to both of us, and you should not be held responsible for caring for me while I heal from my injuries. But I also shouldn't be euthanized.
For a consensual act of conception, you have to imagine by some twist of logic that you were one of the two people who threw my off the building as well as the person I landed on. Now you are culpable for what happened and responsible for my well-being.