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Absolutely. I don't really care about my reputation when it comes to doing the right thing
Of course I would stand up for what I believe in. I would not consider that to be "risking" my reputation.
Questions/statements of this sort make me wonder WTF people think "reputation" means.
I always remember the statement of purpose for Arizona State University: "To build a reputation as a world class school." Not to train up good students, or to meet the educational needs of citizens, or even to provide what the young people have paid for, but only to be known as a school. It's something like "Of all the schools in the world, we're one of them!" When I was a chemical engineering major there, exactly half of my professors said in class that they did not know what they were supposed to teach or how to teach it, and one actually said "You SHOULDN'T expect much from your teachers because we didn't get our jobs by being good teachers." Like it's YOUR responsibility to avoid embarrassing these frauds.
Yes. That never harms one's reputation with reputable people.
Jewels, sometimes it's the next prospective employer that feels that way. That's why many of those whistle blowers have a difficult time finding work after having reported an incident.