Should we come up with tag standards?
The direct answer is yes, absolutely. We do need to curate tags for them to be useful; part of that is making sure our terminology and formatting is consistent. We don't want new users to be confused by tags that all sound very similar and we do want established users to create new tags based on some general standards to avoid duplication and confusion.
Should we be using a common prefix on tags that require them (eg.
If they are redundant, we should discuss which to prefer, and re-tag accordingly. This has to be handled on a case-by-case basis.
In the case of your example, "moderation" is not the same as "moderator" - one refers to an activity while the other refers to a role. The moderator-selection tag can't effectively be replaced by a moderation-selection tag. The moderation-bullying tag clearly refers to the use of moderator privileges or tools for bullying but a moderator-bullying tag would be more ambiguous - does it mean one moderator bullying another? Moderators bullying non-moderators? It could even refer to a group of regular users bullying a moderator. I have seen examples of all three circumstances. (In any case, bullying has now been split off as an independent tag.)
Should we keep (or eliminate) the plural version of tags?
I don't think it would be useful to have a general policy with respect to plural vs. singular tags. As long as they're not redundant, I don't see a problem. These tags will start with the same letters, so the existing tag will pop up right away as you type - if a user's still going to make a duplicate tag at that point, no standard we've set on meta will stop them.
I might tend to favor plural forms because tags are by nature used to collect a set of like items, but this wouldn't be appropriate for proper nouns (the programming language gets tagged python; your pet snake gets tagged pythons). There are also ambiguous cases;moderator-elections could just as easily be moderator-election because "election" in the latter case could refer to either an election or the process of election.
In short, just use your best judgment. In your example, I think moderator-teams is fine; I'm not sure how moderator-relationship is going to be useful either way (plural or singular). "Relationship" is awfully vague.
should we prefer "site" over "community" in tags?
I think this is distinct enough an issue that it deserves to be discussed and voted on separately.