TL;DR without abortion, if governments still want people to have the ability to unilaterally opt out of parenthood after conception, "financial abortions" would be the only option. And that option would very likely to available to both sexes.

Edit: Some people have brought up governments not wanting to financially supporting kids. I doubt that will happen since there is so much demand to adopt babies, any unwanted ones will almost certainly end up adopted. Couples have to wait years to adopt babies. Yes, there are kids stuck in the foster system but those are older kids who are far less desirable to adoptive parents.
Edit 2: Some people scoff at the idea of "financial abortion" because it's never had much backing, but until very recently, women everywhere in the US could unilaterally relieve themselves of parental obligations by having an abortion. That is now no longer an option in many states.

With abortion, reproductive rights are fundamentally unequal, women can opt out of parenthood after conception any time prior to birth by having an abortion. Whereas men have no such rights, they are stuck paying child support if they conceive a child with a woman and she wants to keep and raise it.

Given severe abortion restrictions in many states I think we will see an uptick in women becoming unwilling mothers because the fathers would not consent to an adoption.

This Reddit post is an example of that situation. TL;DR a father refused to allow his ex to adopt out their child, got custody, and made her pay child support.\*

I think conservatives in states where abortion is banned or severely restricted will still sympathize with women who are forced to become mothers because the fathers would not consent to adoption.

Whether you agree with their social values or not, it seems obvious that they oppose abortion because they genuinely think it's murder, and not because they want to force women to raise children they don't want. Because conservatives regularly tout adoption and safe-haven surrender programs alternative to abortion, both of which serve to relieve mothers of their parental responsibilities. Texas state Republicans pioneered this program in the 90s. Even the much-maligned anti-abortion "crisis pregnancy centers" often tout adoption as an alternative.

It seems obvious that pro-life people are sympathetic to the burdens of motherhood and are supportive of options to avoid that burden so long as it doesn't involve the termination of unborn human life.

That leaves "financial abortions" (unilaterally surrendering parental rights and being relieved of parental responsibilities like child support) as the only good option. Essentially, giving them the ability to unilaterally opt out of parental rights and responsibilities, without being forced to pay child support should the other parent want to keep the child and raise it themselves.

And furthermore everyone knows that the main reason women seek abortion is not "bodily autonomy" or "health" reasons but rather, the burden of raising a child for almost two decades. By providing a foolproof way to unilaterally relieve yourself from parental responsibilities, pro-life state governments will be reducing incentives for illicit abortions.

And the kicker is that same right will very likely be extended to men as well. Governments are generally loath to pass laws that are not at the very least facially gender-neutral, because otherwise they would very likely to be struck down as unconstitutional. Safe-haven laws as they exist are worded in a gender neutral way. Even though they were targeted towards mothers, fathers can still legally drop off their child at designated sites without fear of prosecution.

\ Note that mothers cannot always unilaterally adopt out/surrender a child and relinquish their parental responsibilities. If the father registers with the putative father registry, and decides that he wants custody when he is notified of the child's planned adoption or surrender by the mother, he will very likely gain custody barring any serious problems with him. And she will very likely be required to pay child support.*

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