I do consider myself to be raising Jewish children. I expect, for example, my daughters to have a bat mitzvah (boy is this going to be news to them...).
Part of the thing for me is that I've never witnessed a bris ceremony, or really ever heard a Jewish person talk about finding meaning in it -- it just hasn't been part of my experience, except as a source of implied exclusion because of circumcision. But essentially every other aspect of Jewish life has been reconsidered and reinvented across the centuries; Jews who consider themselves deeply religious pray in all sorts of ways and different amounts, and they follow all sorts of different levels of kashrut. (As my old rabbi Larry Kushner used to say, if you won't eat roadkill no matter what a scanner says about its safety and nutritional content, here at least keeping kosher a little!)
When something that Jews used to do doesn't make sense anymore, like obsessing about virginity or enslaving people or forbidding those with tattoos to be buried in a Jewish cemetery, subsets of Jews who totally consider themselves religious change it, and do so proudly. That's one of the things I love most about being Jewish -- at least in the Jewish tradition that I've always felt most clearly a part of, at its core has been an insistence on returning to first principles and refusing to do something just because other people are doing it.
That's always seemed intimately connected to the history of oppression of Jews: there are too many people who gang up on the powerless because they can, but rather than match their violence and cruelty, Jews have insisted on a path that puts morality and respect for life and human flourishing above all else.
Thus you can have a leading rabbi in Jerusalem publicly eat pork in a time of famine, you can have any 13-year-old give a public speech disagreeing vehemently with God's actions in the Torah, and you have an outsized representation of Jews in the world's charitable and humanitarian organizations.
I love Jewish ceremony and collectively experiencing milestones and recognizing traditions -- and I think the most fundamental tradition of them all is the insistence that tradition itself comes second.