I actually just did mine two weeks ago. I shut the door to the room with my BP while it cleaned. However not because of any fumes, but because I opened all the windows/doors to the house during the whole 4.5 hour duration while it was 20 degrees outside, ha.
I'm sure your BP will be fine during the cleaning. I'd only worry about it more so if you've cleaned it with chemicals in the past (which you probably shouldn't be doing to the oven in the first place).
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