So would Not covering your hair be considered part of this?
I would think so. Since it is well accepted by everyone that it is an issur. Even that article by Rabbi Professor Broyde was written as a limud zchus, and in not intended to mean that he thinks that is the halacha (as is clear in the article; I read it).
A funnier question would be something which is a machlokes. If a ger says he will only wear Rashi teffilin, would Rabeinu Taam consider the geirus bad? That sounds weird. But I don’t really see why not.