The doormat issue is an interesting one.
The Cross was worse than a doomat.
Yet, a wimpy, passive, passive/aggressive victim-mentality door-mat-ism is not, per se, Biblical, imho.
But, we must be ready to be and do as God requires of us . . . including things which MIGHT look like being a door mat for a season.
But not out of sick psychology motivations.
Doormat is probably the wrong term. Loving your enemies does not mean doing everything they say. Half my church is my enemy. They want to destroy my Pastor's ministry. I still love them all but I will not join them in their recall vote.