In essence sects shouldn't have any control over one another. The pope can't make Lutherans do !@#$. The supreme Ayatollah has no authority over Sunni Muslims. Having sects exist within a religion that's still beholden to the main religion's authority doesn't make a whole lot of sense.
That's why at least conceptually it makes more sense for sects to be represented by making a mechanic for two religions to be linked in such a way that it's easier to convert from one to another and thus a new opposing philosophy within a religion can quickly gain traction.
We have been using the term Sect to refer to factions within a group. So for example Jesuits would be a sect within the larger Catholic Church. For Lutherians/Catholics, the current mechanics for separate religions are fine, simply set up the relations between them and you are sorted. I really don't believe it is any easier in general to convert a Protestant to Catholicism then it would be to convert them to Buddhism or Islam.
