The loss of community has more serious consequences for the psychological and spiritual health of men, who are oriented to group formation as a part of the vocation. Women at least have the potential to still have a husband and family; they may lack the larger network of other women who can provide psychological support and help, but being a wife and mother defines their natural vocation essentially. But for men, being in an authentic community with other men is a primary part of their natural vocation.
Haid'ts correlation of traits/personality with political stances need to be broken down according to sex, if it hasn't been done already. Peterson is definitely a liberal trying to be a moderate, alt-lite at best. There's a lot of "science" (especially regards to evolutionary biology) here that does need to be examined more carefully -- much of it is probably more philosophy than science.
As for Peterson's Christianity, it is hard to see how he is orthodox. At the very least, he is more of a modern Pelagian, how human beings should activate the divine self from within.
Should there be ascesis with respect to women's mating strategies and status signaling/intrasex competition (shopping for brand names, etc.) or even their expectations? How should these be ordered properly? Do these inclinations just require proper integration through prudence or forms of moderation or both? (How much foresight can we expect women to achcieve?)