Is there any reason this logic can't be applied to religious belief (or lack thereof)?
As long as they are not contradictory it is no issue. Meaning that we don't measure it against something.
For instance:
Our truth statement / belief (Can't change no matter what):
"Stealing is wrong."
Then it doesn't matter whether it is a poor person stealing or someone else. The only correct answer is that "Stealing is wrong", because that is what we decided was true. We might ignore that a poor person is stealing, but doesn't change that ultimately, when we are asked about whether it's right or wrong, and again have to stay true to the statement above, that we would have to say that stealing is wrong, because that is the truth.
The reason for this is because we measure against this statement, just as a religious person measure against their scriptures, and just as the above statement, these can't be wrong. So if a scripture say that there is only one God, then there can't be any other, despite that we might accept that other people believe there is, but based on our belief, they are simply wrong ultimately.