Are Graduate Schools Less Likely to Fund and/or Accept Nontraditional Students?
this is because 40+ year old students rarely get tenure track positions.

False.  PhD students of any age rarely get tenure track positions.

Even at the master's level, however, would I have difficulty getting funding at my age?

Not because of your age; however, PhD funding is more common than master's funding.

Also, are nontraditional students more likely to be rejected?

In most cases, no.  You may experience confusion if the program has never had a nontraditional applicant.