I think you are absolutely right to highlight that 'free choice' doesn't exist in some sort of bubble, and that what we want - or think we want - is partly shaped by the messages we get from society.
HOWEVER...
An obvious critique of 'false consciousness' theory is that it involves an assumption about what a person's 'real' or 'authentic' or 'natural' desires would be vs what are their 'false', 'socially conditioned', 'unnatural' desires are on the other. No doubt you can see how this arose out of Marxist theory. We end up with judgements like 'You can't be working class and in favour of low taxes' or 'You can't be black and want to lead the Conservative Party'. Anyone who doesn't conform to what we think their 'natural', 'authentic' position 'should' be gets portrayed as a brainwashed sheep.
I don't believe that the only reason that some women seek out or accept pre-martial sex is down to 'false consciousness'. Sure, we can point out that men have more of a biological imperative to sleep around than women do, but this is too simplistic a take on humans. Desire and sexuality are complex things. Women have clitorises as well as wombs. Sex can also fulfil a wide range of purposes for women, I think.
I do have some serious concerns about where social trends have taken us - for example, I agree that there is often pressure on women and indeed young girls to do things we would not like to do, and a tendency for women's self-esteem to get bound up with sexual desirability and performance to a huge extent (which is often a double-edged sword, as men seem to sometimes simultaneously hold the views that 'she's only got value if she puts out' and 'she's a disgusting worthless slag if she puts out', so you sort of can't win).
I just don't think you can boil it down to saying that contraception is good or bad for women overall, though. Casual sex has always been around in society. There has always been prostitution and sexual violence and coercion and pressure - these things were not 'invented' as a result of contraception. Unwanted pregnancies were incredibly damaging to women's lives back in the days when 'purity' was valued, as whether the sex had been consensual or not, those women were seen as 'ruined', so there was a huge amount of stigma, ostracisation, shame and yes, of course, dangerous backstreet abortions. And let's not forget that lot of sexual violence, historically and now, has taken place within marriages, so marriage is no guarantee of safety and autonomy. It wasn't really that long ago that a woman who got married in this country ceased to exist as an independent legal entity; her husband had full control of her money and of any children they had together, and even a high level of violence and abuse from him was very unlikely to enable her to separate from him. Is it better when laws and social norms push women and men to only have sex within the tight bindings of life-long unbreakable commitments? I'm not convinced.