The OP asks an interesting question to which immediately comes to mind - it is better to encourage than admonish.....
... also that I am not my brothers keeper(an idea outside Freemasonry), and the masonic virtues of silence and being willing to shed a tear of sympathy on the failings of a brother - but also counterpointed by our great principles of brotherly love, relief and truth and the two core ideas in Freemasonry - improving yourself and treating the people around you well.
The term is to “whisper good counsel”....
We do not have that line - but do have the idea., but I will use it in the future
We have a discussion on this very topic this week - about calling out bad behavior. One factor we identified is we often do not seek to correct a brother due to advanced age or rank - which often come hand in hand.. but also spoke about how it is often people who hold rank or age who need some nudging in the right direction. As a generally conservative organisation with an aged membership, we often meet attitudes out of step with todays society, indeed often positive ones like integrity and honesty, but also (as I see them and it is often subjective) negative ones, especially around sexuality, minorities and even woman - but as an example and I have said elsewhere, holding and voicing a value like misogyny is unmasonic. We have a masonic virtue of silence, but all to often we use that as an excuse not to confront bad behavour, and I often wonder about that. Tempered by the idea that Freemasonry promotes tolerance and acceptance - not judging others. (Especially when combined with my Religion which includes the " Judge Not" idea , (viz Matthew 7:3-5, John 8:7))
...Once I become a Master Mason and see another brother not conducting himself properly to others, can I remind him of how he needs to conduct himself and treat others if needed?...
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Again, it is better to encourage than admonish. While my brothers are correct - you will learn about this as you pass through your degrees, I've often found a question is much better than a statement, and a question might be "Being new to Freemasonry, I was wondering how that behaviour is consistent with being a Freemason" or "Are you being the best Freemason you can be?" - but as a newbie you might be received as a smart-ar@# asking a Brother that sort of thing..
One thing I do know, I am less likely to tolerate poor behaviour within Freemasonry and from Freemasons than I am in wider society, especially business.
But I guess all that is really no answer at all to your question..