The promotion evaluation system is supposed to be based on objectives and facts.
Usually, you have to set metrics and objectives on which the manager is supposed to rely on with him.
The emotional aspect can be part of keys to improvement if it's not something grave.
However, good managers will know that this aspect is not rational and can't be fully relied on (person not liking other's face for example).
To come back to your question:
- On the email case, don't give others means to misunderstand it, be factual and objective. In the worse case, they'll say that you are an emotionless robot :)
- On the comments, you'll need to validate whether it's perception or bad-faithed people.
Following if the comments are based on perception or if it's people who are people others down, you should:
- Perception: Adapt to your interlocutor based on his/her feedbacks when you interact with them. Funny Data science Example: Don't suggest a dataset about how good meat is if your interlocutor is vegan
- Bad-faithed people: you'll have to put them in front on their lies 1-on-1 with a neutral witness and remind them kindly that diffamation against someone is not professional at all and is punished by the law. The neutral witness is very important as the bad faithed-person can transform everything you said. By doing this, you are making the person acknowledge his/her mistake and highlighting the consequences of such behavior.
Already lived this situation and in the end, IMHO, that's the best approach I found through failures.
You can't go against people instictive perception as it's usually the result of their lifetime construction and experiences. You just have to adapt to it as you say "Sir" as a sign of respect.
I tried the nice way several times with bad-faithed people and ended-up always getting backstabbed. They usually forget that diffamation is illegal and that they can lose both professionally (would you trust a ressource that lies ?) and personnaly (court decision).