Can I bake a pie and a savory dish in the oven at the same time?

I agree. Would ask myself - a. Will the same baking temperature work for both?
B. could the flavour/aroma of one affect the flavour of other. Example if your savoury dish is garlicky, I would be wary. C. Will there be any contact of any sort... Dripping/overflowing/leaking pans causing the dishes to touch would be worry some.

If they are both at the same oven temp it should be ok. Just be careful, if you are making a fruit pie that might drip, bake it on a sheet tray so it doesn't drip on your savory item