As a hiring manager do you look at candidate's GitHub Profile

I manage teams at Amazon and personally, I will look into the GitHub profile if they have called it out on the resume. But I do it only to understand the candidate's interest and not as a hiring decision point. Amazon interviews look for leadership principles and technical skills (more specifically, coding on whiteboard, system design within 30 minutes etc.). There is a lot more emphasis on quick thinking, being able to understand what the interviewer is looking for and focus on that, asking questions to disambiguate the problem etc., none of which are answered by the GitHub profile. Further, a lot of senior engineers would not be active on GitHub.. Most of them are already working full-time elsewhere and it would be unfair to them to consider what they do in their free time as a hiring decision point.

We can argue if the interview is fair and provides the right set of candidates, but that is going to be pretty much a different discussion.

Yes. I don’t see why they’d have a public profile if they didn’t want people to see it.

I'll review it and use it as a data point but I don't make any decisions solely based on it.

More importantly, I don't hold it against anyone who doesn't have one as many times mid career and/or senior candidates don't. Or when they do it is sparse or dated.

There are nice parts to seeing one. I've used code from the candidates profile and had them walk me through it and used it as a tool to learn how they communicate.