Most people call that ISFJ. Except in Socionics. Socionics is the theory that calls this Si dom the ISFp....except most people here aren't going by Socionics, so I'm baffled by it. Especially since in Socionics Si has so much to do with comfort and health.
I am very P. I am a big huge P, on most tests I score P the highest letter, and my life is very much evidence to this Pe perception. But because of my sometimes rigid Fi judgments some people think I seem J. And it's kind of like, NO, you see me as "J like" when I make rigid Fi or Te judgments because I'm seeming then more TJ-like, not FJ-like.
I remember Simulated World trying to explain this to somebody, that FJs look more outwardly rigid, but that FPs are actually more inwardly rigid because of Fi, despite their external flexy-ness.