how to respect older/elderly people who are conceited and demand respect because of age? How to respond appropriately to people that are significantly older than me if they demand respect because of their age yet are conceited (and typically also conceited about not being conceited)?

Often old folks use their age to gain respect, and then build their authority on top of it to spread false teachings. How would a passionate person handle such situations, not wanting to offend against the Dhamma by insulting the older/elderly person, yet preventing them from getting away with conceit and/or false teaching?

How would the Buddha have handled such situations?

I think a lot of Christian folk use such coercive tactic to gain authority and following, so I think it’s a practical question in the western world.
Situations triggering resentment present challenges. To abandon such resentment and act freely requires mindfulness of body, speech and mind. For example, the conceit you describe is heard and resisted as coercive, impure speech. In this particular case, Venerable Sāriputta details the following advice:


  AN5.162:2.5: In the case of a person whose behavior by way of speech is impure, but whose behavior by way of body is pure, … you should get rid of resentment for that kind of person.


This alone is astounding in its uncompromising assertion that it is our own resentment that is a hindrance needing to be abandoned. Venerable Sāriputta continues and provides a more detailed example:


  AN5.162:4.2: Suppose there was a lotus pond covered with moss and aquatic plants. Then along comes a person struggling in the oppressive heat, weary, thirsty, and parched. They’d plunge into the lotus pond, sweep apart the moss and aquatic plants, drink from their cupped hands, and be on their way. In the same way, at that time you should ignore that person’s impure behavior by way of speech and focus on their pure behavior by way of body.


In this way one may gently ignore the strident teachings of such people while praising their silent kindness, caring and generosity to others. If you're curious, AN5.162 has more detail for study.