We are mammals. All mammals reproduce sexually by having two sexes, female and male. Male bodies are organised around producing small gametes, i.e. sperm, once the individual is sexually mature. Female bodies are organised around having large gametes, i.e. ova or eggs, and having the body parts to gestate an infant, give birth and then produce milk to feed said infant, again once we are sexually mature.
That's the biology, and it's hard fact. It's not possible for anyone to change it, nor for anyone to change their own sex. Understanding this doesn't make someone conservative, any more than it's conservative to know about gravity or that the sun rises in the east and sets in the west.
It's perfectly possible to understand the biology and also to think that women and girls should be able to control their own fertility. Just because we can reproduce doesn't mean we have to do it. It's also perfectly possible to grasp that gender stereotypes are socially constructed, unlike biology. We know this because they've varied over time and from one society to another. We don't have to abide by them if we don't want to.
Conservative is a label used to indicate someone wants things to stay as they are. Liberal is a label to indicate people who are more open to change and progressive ideas. These labels are all about political, social and economic attitudes and nothing to do with science. It's unfortunate that they've become tangled up with science.
It suits some people to ignore hard facts when it's inconvenient to acknowledge them, and one of those is that men and boys are responsible for almost all sexual crime and most violent crime, and so when it comes to safeguarding women, girls and other vulnerable groups, sex matters. Not all males, but far more males than females, commit these crimes.
Sex also matters in sport, given that sport is all about what the human body is capable of, and male bodies, not hampered by the need to maintain the complex female reproductive system, are usually stronger and larger.
We have constructed a world where the default human is male, and women and girls are expected to fit in and make the best of things even though our very different bodies and reproductive roles make that hard or even impossible in many cases. There is nothing conservative about saying that women are not second-rate men, nor are we weak. We have just as much right as men to want our needs and desires to be taken into account in how we structure our society.