RSS excluding problem

WordPress, for some reason, excludes posts from the RSS feed when they are tagged in one specific category

No it doesn’t. Have you tried:

– deactivating all plugins to see if this resolves the problem. If this works, re-activate the plugins one by one until you find the problematic plugin(s).

– switching to the Twenty Ten theme to rule out any theme-specific problems.

– resetting the plugins folder by FTP or PhpMyAdmin. Sometimes, an apparently inactive plugin can still cause problems.

Could you point me towards some files in WP code where I could look into?
Because I can’t just deactivate all of the plugins on a live site.

For example, let’s say the category name is “video” – full feed doesn’t show posts in that category, but if I look into, say, feed for category “other”, it will show posts that are tagged as “other” and “video”.

If your feed is excluding a specific category, then it’s either a plugin or your theme. It’s definitely not WordPress core doing this.