If Don't Tread On The Bear is failed, will quests like Return To Sender also fail or is it only the For The Republic quests? Also, can I confirm that NCR reputation will not be lowered if the reason for failure is due to the Courier siding with Yes Man/Mr House. My current NCR reputation is Idolized, Strip reputation is Idolized and Caesar's Legion reputation is Hated (I failed Beware the Wrath of Caesar by stopping the King's for COL Moore).

Only the "for the republic" gets locked, and you lose a little rep. With Idolized you are more than fine.