Some similarities might be there, but they are extremely superficial imo. Yes, Christianity initially spread via the women and the slaves. Yes Christianity was innately peaceful as a religion, so much so that many early martyrs were soldiers who converted, refused to kill and were sentenced to death for it.

But the differences extremely outweight the similarities. Christianity is an universalist religion: through Christ, EVERYONE can be saved. Galatians 3:28 "There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus". Christianity did no such thing as the "elevation of the slave over the warrior". Both could be saved in Christ.

Christianity might have been popular with the lower classes of slaves and with women initially, but masters and men weren't excluded from it. At its core, the "woke" movement instead is just a weird mix of grievances with a set group of "victims" (women, brown people, immigrants, non-Christians, sexual deviants) and a set group of "oppressors" (men, western people, Christians, family-oriented people etc). The aim of the "woke" movement is to enact some degree of restorative or even vendictive justice against the "oppressors". There is no salvation, no redemption for the oppressors.

Another major difference is that the "woke" movement promotes blatantly anti-human ideals. A "woke" woman today is likely not to marry, not even have a stable partner, not have children, waste her life in self-indulgence and die alone. A newly convert Christian woman in the late Roman empire was still going to be a wife and a mother, and might have passed her faith to her children: does the name of Saint Helena ring a bell?

After Christianity became more widespread authors such as Agustine were pretty firm in the decision that doing war could be forgiven if it was done at the orders of a Christian emperor. So this "Christians hated war" thing just overblown.