Cookies Manager+ v1.10 introduced a new feature: read-only cookies data.
This feature saves the read-only cookies data by default in encrypted format. Because of that if browser has master password enabled it asks for the password on browser's startup or when CM+ window opened.
The solution for avoiding master password prompts is to disable read-only encryption in CM+ options:

Note, that without the encryption, potentially sensitive cookies data will be saved in plain text.