Stuffy English teachers are famous for promulgating the idea that we shouldn’t put anything between the “to” and the verb when you use an infinitive. A guy name or Robert Lowth was the origin of this, by the way. (cf the post for March 14)
Anyway, the meaning is subtly different between splitting and not splitting that infinitive.
Charlie stuck his head through the dive shop door. Karen appeared to be waiting on someone in the military, so he slipped in quietly, to not interrupt.
Charlie stuck his head through the dive shop door. Karen appeared to be waiting on someone in the military, so he slipped in quietly, not to interrupt.
The first selection says he doesn’t want to do something, period. That second one, though, implies that you have an alternative verb in mind, such as
Charlie stuck his head through the dive shop door. Karen appeared to be waiting on someone in the military, so he slipped in quietly, not to interrupt, but to be sneaky.
See? It matters. So write what you mean, and forget about Robert Lowth.