usage - Is there a context where 'to neglect' and 'neglecting' are not compatible?

Neglecting others means ignoring [them].

I think you mean an object there, or the sentence would sound odd to my ear. In most cases where the gerund or infinite is the subject of object of a verb, you can replace one with the other (I can't think of an exception).

However, a gerund can be the object of a preposition, while an infinite normally cannot:

After conquering Athens, Augustus paused.

After *to conquer Athens...

There are also many verbs that only take one or the other. Lastly, there are cases where the two have different meanings:

Cleopatra stopped looking at Marc Athony. = "She had been looking at him but now began doing something else."

Cleopatra stopped to look at Marc Athony. = "She stopped doing whatever she was doing in order to look at him."

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