How to include quarterly regressor in Prophet for monthly time series?
You have to evaluate based on your business problem, but there are some questions you can ask yourself.

How are the external regressors making their predictions? Are they trained on completely different data?

If not, are they worth including?

How quickly do we expect those regressors to get "stale"? How far in the future are their predictions available? How well do they perform more than one quarter into the future?

Interpolation can be reasonable based on these factors...but don't leak information about the future to your model at training time.

Do they relate to subsets of your features?

If so, some feature engineering could but fun - combine the external regressor's output with your other data in meaningful ways.
I have a monthly time series which I want to forecast using Prophet. I also have external regressors which are only available on a quarterly basis. 
I have thought of following possibilities - 

repeat the quarterly values to make it monthly and then include 
linearly interpolate for the months

What other options I can evaluate?
Which would be the most sensible thing to do in this situation?