For me, it's always a bad idea for me to use a deep conditioner when I have extensions. Creamy conditioners tend to not wash out completely so they get caught up at the roots where the extension was added to the hair. Then, when I have to take them out, it's a struggle with tangling and white stuff caked up at the roots.
So with braids, I wash with a moisturizing shampoo applied to my roots. I rinse really well. Then I spritz my hair with a moisturizing water based spray and let it dry. I spray daily to re-moisturize. When removing the extensions, it's a breeze to remove.