Catholic theology is that humans are a unity of body and soul. There are two different ways of having a body: male, and female. Both are good and part of God's plan. Sidebar: claims that Aquinas and Augustine called women "defective males" or similar are incorrect and based on mistranslations of the original writings which I believe were in Latin (not a theology scholar or anything).
In Catholic theology, suffering, disability, and death, are consequences of Original Sin. Although many people think of Original Sin as saying that it's your own fault if life is cr@p, it's essentially saying the opposite: we are meant to have a good life, but because of this implacable factor of original sin, sometimes we don't. Because of the wounds inflicted on us by original sin, we need healing (Jesus Christ, basically). OS is not a science concept, it's a metaphysical concept. With this concept, gender dysphoria is something that causes suffering that is not your fault. The suffering is from the dysphoria, not from having the "wrong" body. Gender dysphoria would be in the same category as any other suffering inflicted by illness/disability, e.g. measles, lupus, etc.
There isn't a final answer yet by the Catholic Church on what types of treatment for gender dysphoria would be licit - there are some documents but a lot of pushback, so it's in flux. Bodily mutilation normally is illicit but women can have mastectomies to treat/prevent cancer, because of "law of double effect." So mastectomies are not always disallowed. Likewise, opposite-sex hormones - lots of people take hormones licitly for other reasons e.g. HRT for menopausal women, Thyroid hormones for hypothyroid, etc. So cross-sex hormones is not a clear cut thing either. But you have to balance risk and benefit and part of the key is what does healing look like? If you are born male, then Catholic theology would be that being healed would mean being happy in your male body. Trying to become female if not born female would not be a type of healing, and would be impossible in Catholic teaching.
That's a basic overview but Catholic theology on such issues is complicated. But a definite thing is that male cannot become female because that is how God gave us our bodies and to be born male is not a disability, nor is being born female a disability. (i.e. You can't heal what's not broken).
By this reasoning, Catholic Church should be against allowing males to be in private spaces of females, e.g. where females get undressed etc. Some liberal Catholics apparently are opposing this. I have been trying to figure out why. I think it is basically about 'Be Kind" and the idea that Jesus wouldn't exclude anyone. I haven't quite worked out why Catholic pro-gender-ideology advocates think it's ok to expect women and girls to accept males in our private spaces, but if I extrapolate from the arguments I've seen used by liberal Catholics who agree with gender ideology, the basic idea would be that girls and women should be willing to make a sacrifice of our private spaces to save the lives of transgender people who would otherwise be suicidal. Again, this would be a distortion of Catholic teaching but you wouldn't know that if you didn't understand what the Church teaches about matters where sexual differentiation is important. This is another matter in flux and I'm fighting hard as a practicing Catholic to make sure my voice is heard speaking up for women and girls.