Do Native Help cards apply when replacing another player's settlers?
Yes they do.  Looking at rules from link here it says the following (emphasis mine)

Native Help cards have the following permanent benefit: Whenever you
use a location that includes the depicted icon in the circle, the
required number of settlers you need to place on this location is reduced by 1. If you have several cards of the matching symbol, each
of them reduces the required number by 1. However, you must always
place at least one settler.

Earlier in the rules the term 'required number' has two definitions.  One is the number printed on the board.  The other is the number of workers on a space plus one.  BOTH are consider a 'required number'. So if that is the case the benefit of the native card applies in both situation you describe.
Secondly there is this thread on BGG where a user says they asked the publisher your same question and it was answered-

Yes they do reduce the number of settlers needed to bump another
player from a tile to a minimum of 1.