I noticed people playing in the 1.3 glitchless category didn't have a code lock on the door. Whenever I did the same run on the same preset I still had to use the padlock code. Can anyone tell me why that is, and how I can remove it too?

It's because they're on easy difficulty - easy doesn't have the padlock code.

If they have they speedrun mod installed, then you can see what difficulty they're on by looking at the end of the run.