Of course they wouldn't say it out loud: that would be giving the game away. Instead, judge them by their actions. The same crowd that wants to prevent abortions also wants to prohibit contraception, allow unrestricted gun ownership, and cut back on any social programs that support families.
These actions are consistent with a puritanical, anti-sex society; they are not consistent with a "commitment to life."
Stop listening to what prochoicers say prolifers believe, and start actually listening to what the prolifers are saying. I (and most prolifers I know) don't have some secret agenda.
When the cop beats you bloody while declaring that it's "For your own protection," you are justified in questioning his motives. When the right claims to care about "life," but their actions totally contradict the stated goal, I get to declare them at best hypocrites but more likely just fascists.
I see this kind of thought process all the time: when some people don't get traction with their arguments on a particular issue, they ascribe other beliefs to their opponent and call those into question. This is both ad hominem and whataboutism, and it doesn't win over anybody's heart or mind, it just "others" the opponent, further entrenching tribalism.
The "crowd" is diverse and contains multitudes. If you want to change minds, engage with the arguments, not with the arguers.
If you don't want to be judged as a tribe, you need to take a stand. If you support contraception and gay marriage, then support them. Right now, though, the right is supporting more and more extreme ideologues.
Just because you believe this doesn't make it true. I struggle to believe that a single pro-lifer would say this is the reason behind their beliefs. As a pro-lifer, I can attest that it has nothing to do with my beliefs. Believing it may "demonize" prolifers, and help you feel good about fighting for your stance on abortion. But the reality is, blind beliefs like this are the cause of division and hate that seems to be ever increasing.