However, having one gives the interviewer some additional insights about you. While no candidate should be discarded for not having public code, I don't think dismissing it completely without even looking at it is correct, because you are discarding a great source of information about a candidate.
Note that the insight could even be negative (such as a candidate applying to a senior position with sub-par public code recently written)
Demonstrating professional skills shouldn't be discounted just because someone else doesn't.
It absolutely should make a difference if it's relevant even other people have reasons for not doing the same.
Hiring is selecting the right person and not selecting the wrong person. It is not about sorting all people 100% correctly into hire/no-hire groups.
A blog with code can tell a lot about a person. Do they understand the material? Can they write coherently about it? Can they target an appropriate level of audience with that? Maybe these can't be answered just by reading the blog, but it gives a lot to discuss in the interview process.
Some people want to have the exact same interview process between all people. People are different, though. Locking the interview down to a single process doesn't allow for the variety of skills out there to shine individually. If that avenue is through a portfolio or blog, it's fair game.
It's not bias to hire non-one-dimensionally. People are not cogs.