The only way to avoid the problem with quotes and emojis is to disable WordPress emoji replacing. To do that, install one of many plugins available to disable this WordPress ‘feature’, like Disable Emoji from WordPress.org repository.
The problem is caused by the Italic BBCode due to the conflict with the Underscore templates system BuddyPress uses. There are two ways to solve this:
- You can disable Italic BBCode (Forums -> Tools -> BBCodes -> Disable BBCodes) or,
- You can limit BBCodes to the bbPress content only (Forums -> Tools -> BBCodes -> bbPress Only). If you do this, BBCodes will work only with bbPress topics, replies and forums.