Just CC in the manager, if they’re being rude or not replying to you, escalate the issue with the appropriate person!
For emails I always found escalating it to someone higher up works well to get a fast reply

For face to face arseholes remember they’re usually insecure, don’t put up with any shit, just use company policies to get rid of the fuckwits
This is one of the things that is making me dread finding a new job and going back to work, all the arseholes. I can’t handle being spoken down to and being treated badly. I see red. I come across as this quite shy person, but when people push me too far, I flip and show them I’m not to be pushed around. I’d just love to find a job one day where I don’t have to constantly deal with arseholes.
Walking away helps, also treat them exactly how they treat you, but be nice it drives them mad!
If it’s someone in a superior position, stop making their job easier and show them exactly how much of an arsehole you can be, when spoken down to
If it’s someone in the same role, do your best to ignore them, treat them like they don’t exist, but also use your company policies to deal with anyone treating you badly!