Propeller Characteristics at Different Altitudes Assuming I have a propeller with a given diameter (D), pitch, blade twist, and number of blades, I can theoretically analyze discrete airfoil sections in XFOIL and come up with lift and drag polars for the airfoil sections, for a given Reynolds number. Using the new information along with the pitch and twist (to give angle of attack for each section), the overall thrust and torque for the propeller blade can be solved for given operating conditions (RPM and airspeed). Even more accurately, the induction airflow factors can be accounted for to adjust the velocity vectors and angles of attack experienced by the airfoil sections on the blade, and an iterative solution can yield more accurate thrust and torque data for the propeller. Doing this at different operating conditions (RPM and airspeed) can give many data points, allowing for a generation of a thrust, torque, and efficiency curve vs advance ratio. I have done all of the above for a certain propeller.

However, if I wanted to change my flight altitude (and thus air density would be different), my Reynolds number could be vastly different for the same operating conditions. Does the thrust, torque, and efficiency curves for the propeller still hold up? Or does the different Reynolds number mean that if I solved the airfoil sections thrust and torque data again, they would yield different dimensionless data as a function of advance ratio?

I'm happy to provide more details. Looking forward to figuring this out!
Your lift and drag polar is Reynolds number dependent. You need to check if you are happy with what XFoil generates for you. Airfoil characteristics are fairly constant over a wide range of Re, so it might not effect you at all.

Also, if you are running high tip speeds, there is another pote increasing altitude drops the temperature as well, so you are increasing the tip Mach number, which you need to make sure stays within the validity limits of your calculation method.