Adopted dog won't come out of crate for walks/bathroom

I just adopted my dog from a shelter last week, and she is comfortable both in and out of the crate both when I'm home and not. However, when she's in her crate (door open) and it's time to go on a walk/go out for bathroom, she won't come out no matter what. Her favorite treat doesn't work, using the leash to guide her out doesn't work, and coaxing her out verbally doesn't work.

How can I get her to come out of her crate? Do I need to stop using the crate or something? If I can't get her to come out for walk/bathroom before I leave for the day, is it safe to leave her in her crate until I come home for lunch without her having gone for walk/bathroom?