So”right”:
Take a look at the Rema YD 178:1.
Chukas Hagoyim only applies to things which are done for pritzus, like wearing red clothes; and things which make no sense, since we are concerned they are avoda zara.
Opening the door for someone is not done for pritzus, and we know why it is done. It is done because it is romantic. And no, romance is not pritzus.
So we can forget that line of “reasoning”.