I got married in 2018 and my husband is currently a non-resident and not filing a CAN return. Can we claim separate principal residences for this tax year?

You only have to claim a “principal residence” when you are selling it, and at that time you’ll get the option to say that you lived in the residence for different periods of time.

If you are referring to a provincial rent/property tax credit, then since only you are doing a return, only you will claim that credit.