Oh yawn, such a lot of disingenuous DARVO on this thread. Notably from one very angry person who is spreading disinformation about "gc" feminism in particular. I wonder why. Could it be they know they're losing?
Anyway, what you've stated here is utter crap. Of course there is a conflict. The two are directly opposed.
Feminism was always about the liberation of women and girls from patriarchy. It centres on women and girls. The material reality of female lives and women's legal and equality rights the world over. Which for centuries were deemed secondary to the needs of men.
In the UK, we were treated as male property until frighteningly recently and still are in many countries. Not based on our "gender identity". Chosen for it because of our biological sex. How we "identify" is neither here nor there to a misogynist who thinks of us as a second class citizen who is there to serve him and will treat us so.
Men who identify as women have NEVER been members of the group who this happens to. They fetishise our oppression as their "identity" instead. All the rights gained for women in the last few decades were gained BECAUSE of what you call "gender critical" feminism aka actual feminism. Many of us grew up with it. It may be new to you, you are clearly ignorant of it, but that's your problem and your poor education. Not evidence that we're something "new".
As part of fighting the patriarchy, feminism fights "gender", which is regressive stereotypes about the way women and men are "meant" to behave. Much of which is oppressive. Such as the idea that "real women" are supposed to display "subservient" traits etc and any woman who doesn't therefore can't "really" be a woman.
Transactivism loves this idea though. It elevates "gender" (backwards sex stereotypes) over and above the material reality of sex, seeks to replace sex with it law, and in doing so destroys all the rights women had to fight so hard for. It has been busily sending us back decades.
Trans IS the patriarchy. In a dress. Men colonising and fetishing womanhood (based entirely on the regressive sex stereotypes that actual feminists ditched about six decades ago), the destruction and demonisation of feminism and feminists (because we fight the very sex stereotypes that form the bedrock of transactivism and offer an alternative that doesn't promote extreme body modification, medicalisation of gender nonconformity or gay conversion, unlike trans).
Women who claim they are "inclusive feminists" are a) not feminists because they clearly don't get the entire basis of feminism or why it arose and b )have instead been persuaded to fully subscribe to the patriarchy by pandering to men and regressive sex stereotypes over and above both themselves and other women. It's pure ignorance.
Meanwhile, a remarkable number of trans activists, particularly "trans women" spout the same misogynistic abusive rhetoric at women who stand up for their legal rights as do other abusive males like incels and male domestic abusers. And their enablers turn the other way. Despite the wealth of evidence that "trans women" have very similar crime rates and types as other men, against women specifically. More so in some cases.
So for the love of god, you and the others attempting to gaslight and spread disinformation on here, stop talking such utter shite.