My opponent has Galarian Weezing with "Neutralizing Gas" Ability in play. Is the "Top Entry" Ability still allowed as a method of benching a Pokemon, or can it not be benched?
You can still bench it. The Top Entry Ability is used before the Pokemon with that Ability is "in play".
Source: TPCi Rules Team (2021-01-21)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH2_8
SWSH2_8
SWSH2_32
SWSH2_32
SWSH2_61
SWSH2_61
SWSH2_113
SWSH2_113