I moved abroad during the tax year, I do not have a Canadian address anymore, but the website is asking me to input a Canadian address to file my return?

You should use whatever address you can get easily get your mail from. So, most likely you would want to use your current address.

The issue is that it's not letting me add an address outside of Canada. What do I do?

Please answer YES to the question "Is your mailing address outside Canada?" to be able to enter a non-Canadian address.