Jakub, you should read the arguments of atheists against abortion. As a Christian, it is not my religious beliefs the impact my view of abortion, but rather my "secular" beliefs, which I share with the atheists that express concerns regarding abortions.
Science and medicine both say, human life begins with conception. You can't escape that, no matter how inconvienent. This is science not relgion.
Nations and politicians have argued "personhood" does not begin until later, but "personhood" is a legal construct not a biological one. So it is one that can be "legislated", but doing so does not change the biological reality of the unborn baby. The term "fetus" means unborn baby, it is not a reference to some other life form.
Some pseudo scientists argue that unlike all other life forms on the planet which begins at conception, human life begins when humans act "cognitively" (of course, that suggests it is okay to kill people in comas, but let's not have that debate). Again, there is no scientific basis to labeling a stage of human development differently than other life forms. For example, are life forms without cognitive function not "alive"?
Simply said, when addressing abortion, it has to be done in the context that one is dealing with one or more human beings including the mother. Any other argument is simply self delusion. One can make arguments for abortion, like if no one wants the baby, why should the baby be brought into the world? That is an argument, but arguing the baby is not human and thus entitled to human rights is something I think most people if they look deep inside themselves don't believe... it is a coping mechanism to deal with horror of abortion even when it is necessary.
Athesists against abortion argue that the unalienable rights we as human claim attaches to our "humanity" and not some other future date. Our legal rights attach at "personhood". And our citizenship rights attach at birth. Again no religion is involved in any of these points in time, conception and birth are biological events, personhoold is an arbitrary one (which is why it is the one up for debate in the various state legislatures and the Congress). They are not arguing when a baby is born, nor will any arguement about when life begins get very far.
Atheists against abortion argue that denying anyone human rights is grounds for denying anyone human rights. China could easily and has argued what they are doing to the Uighurs is for the good of the nation. That the rights of the Chinese as a people take precedence over the rights of the Uighurs as individuals. Anytime, a society denies human rights, it converts a "right" to a privilege. Some people have the right to life and others don't.
Does that mean a society has no right to allow abortion? No, societies violate human rights all the time. Generally, the argument for doing so is that violating human rights is for the greater good. We often kill innocent people in war, on the premise that as long as their deaths are "collateral damage" and not "intentional" then it is a tragedy but not war crime. Abortion fits in this construct. When done on an elective basis involving a healthy baby, it is always a human tragedy, but not always a "crime".
Whatever decision one arrives at regarding abortion, one must recognize that someone's human rights are going to be denied. In Roe v Wade, the court argued that the mother's rights took precedence to the baby's rights, not because the baby did not exist as a human, but rather it could not survive independent of the mother and the mother had no obligation to provide (for lack of a better term) "life support" to the unborn baby (this raises the issue of when we finally perfect the "artifical womb" will couples have the right to adopt an unwanted baby have the baby transferred to an artificial womb? The science is getting pretty close and with 20 years, we should be able to provide such an environment for babies past the first trimester.
As a final note, the Supreme Court's recognition of the baby's humanity and human rights was highlighted when it made clear that once the baby was viable, the mother's rights could be subordinated to the baby's rights but not because the baby was no longer dependent on the mother and so the mother lost any right she might have to terminate the baby's life, but because at viability the baby aquired the "legal" rights of personhood which include the right to have the baby's life protected by the government.
What pro choice people see as a debate on "reproductive rights" really is not. No one argues a woman with a "dead baby" in her womb can't have an abortion. All of the arguments relate to the very humanistic belief, that humans have human rights... no religious belief needed. Most Christians I know believe killing people is wrong even unborn babies, and while this belief is reflected in the Bible's ten commandments, thou shall not kill. Its application to abortion rests on the "humanity" of the unborn baby, not some other criteria... and that very humanity is the reason many atheists feel the same way.