Planned Parenthood does a lot of things other than abortions. So they just have to make sure that none of the federal funds they get go towards abortions.

"Here's how I look at this," Warren said. "I've lived in an America where abortions were illegal. And understand this: Women still got abortions. Now, some got lucky on what happened, and some got really unlucky on what happened. But the bottom line is they were there."

Warren went on to explain how the Hyde Amendment and other attempts to restrict funding for abortion services disproportionately impacts "the women who are most vulnerable":

Under the Hyde Amendment and every one of these efforts to try to chip away or to push back or to get rid of Roe v. Wade, understand this: Women of means will still have access to abortions. Who won't will be poor women, will be working women, will be women who can't afford to take off three days from work, will be very young women, will be women who have been raped, will be women who have been molested by someone in their own family. We do not pass laws that take away that freedom from the women who are most vulnerable.

We need a President who can strengthen women's reproductive rights.

While religious reasons are a major motivation for opposing abortion, opposition isn't in itself a religious belief or practice. Nor does any religion that I'm aware of require you to have an abortion (it might be different if one did). So it's not legally considered as establishing a religious belief.

Honestly, it get weird on this sort of thing any way you slice it. You're in the category where religion and philosophy overlap. Everyone's going to have some philosophy that tells them how to value human life and human rights and all that, and many of those philosophies are influenced by religion (keep in mind atheism is legally a religion). It would be almost impossible to carve out what is pure philosophy and what is religion.

Morally, this seems right to me. Even if you are pro-choice, none of the moral arguments that justify legalization of abortion (body autonomy, the fetus is just a clump of cells with no humanistic value) justifies making someone else pay for your abortion.

If you are completely opposed to all federal funding for healthcare, then your logic is fine. Nothing justifies making someone else pay for anyone else's healthcare in any circumstance. But if you are ok with Medicare, Medicaid, Obamacare, private health insurance, or any other arrangement where one person pays for another person's healthcare, then abortion should be included in that category (if you are pro-choice.)

If a fetus is just a clump of cells with no humanistic value, then abortions should be free the same way that cancer treatment is free. A tumor, even a benign one, is also just a clump of cells with no humanistic value that should be removed.