It reduces the password strength by at most two bits. For passwords made solely of non letters there is no reduction in password strength.

It's one bit per alphabetic character, isn't it?

No, it's only one bit for the first character and one for the second. The case of every other character is maintained relative to the second character, so the parity there provides the one bit of information for each subsequent alphabetic character.

Whoops, I didn't notice that the two L's were still capitalized in the normalization example a few comments up.

*and one for the caps lock key

It reduces the space of passwords just as much as having the backend try those same combinations for every query.