The implication is that those of us who choose/have to work outside the home are only mothers for part of the time rather than 'full-time'.
Generally, I don't think that there is such an implication, more an inference on the part of those who don't like the term.
In actual fact, being in an office/school/lab/supermarket doing a job does not mean that we are not parents during those hours. We also have to do everything in terms of school runs, homework, housework etc that SAHPs do for their children, on top of our other jobs.
I don't think anyone would actually argue that parents who have paid employment aren't parents during the hours they are not with their children. However, it's patently not true that all working parents do "everything" that most SAHPs do for their children - younger children are often in nursery or with childminders, school-age children are often in before and/or after school club where their minute-to-minute care is taken care of by paid professionals. Unless the working parent is in childcare or works school hours only then there will be some aspects of their parenting role which are outsourced.
As I've said, I don't really have a dog in this fight as I am neither, but I think your implication that working parents are able to somehow fit in full-time work alongside everything a SAHP does is the reason that SAHPs do feel judged.
Your insistence that 'nobody' is judging them is undermined by your accusation that they are being patronising and self-satisfied for suggesting that staying at home with their children is just as legitimate a use of their time as working.