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It's also important if you're checking hashes (at least, it was - if you're using correct hashing algorithm that isn't ancient, you will not have this problem).
Because if you take for example "0e462097431906509019562988736854" (which is md5("240610708"), but also applicable to most other hashing algorithms that hash to a hex string), if("0e462097431906509019562988736854" == 0) is true. So any other data that hashes to any variantion of "0e[1-9]+" will pass the check, for example:
I did use md5 as an example because the strings are pretty short, but it's applicable to a whole lot of other hashes. And the problem is that if you use one of the strings that hash to a magic hash in a vulnerable site, it will pass the password check for any user who's password also hashes to a magic hash. There's not really a high chance of that happening, but there's still a lot of hashes that do hash to it.
that is terrifying
If you're checking passwords, you should be using constant time string checking, anyway.
More likely, you should let your bcrypt library do it for you.