One could probably do linguistic archeology on the exact meanings of the words “serve” and “master” in the original language the quote would have been written in. I’m curious if the exact words would be cross-applicable with one’s parents. But in a larger sense, no, I don’t personally think that one serves one’s parents. One is raised by one’s parents, and may even be expected to be obedient to them, but to “serve” as one serves a master isn’t to my mind an appropriate way to think of one’s relationship with one’s parents.