Say my opponent uses Trevenant & Dusknoir GX's "Pale Moon GX" attack on my Keldeo GX with "Pure Heart" while Power Plant stadium is in play. If I replace the Power Plant with another stadium during my next turn, does Keldeo GX get knocked out at the end of the turn or not?
If Keldeo GX remains the Active Pokemon it will be Knocked Out. Keldeo GX's Pure Heart Ability *prevents* effects, but it does not *remove* existing effects. If an attack like Pale Moon GX places an effect directly on Keldeo GX, that effect cannot be removed by reactivating Pure Heart; in other words, effects that are removed when returning to the Bench can't be removed by Pure Heart.
Source: TPCi Rules Team (2020-01-09), TPCi Rules Team (2020-02-06)

Relevant cards

Note: All applicable cards may not be listed below.
SM10_183
SM10_183
SM11_219
SM11_219
SM11_240
SM11_240
SM11_47
SM11_47
SMP_SM217
SMP_SM217