Yes, they should be tagged harry-potter.
While Harry Potter and the Methods of Rationality is a particularly well-known piece of fanfiction which has its own tag and a dozen questions about it, there are untold thousands of other fanfictions which are never likely to have more than a single (or even a single) question about them on this site. If someone does want to ask a question about a random little-known HP fanfic they've found online, I think it makes more sense to tag it harry-potter and fan-fiction than something like the-golden-snitch-a-dramione-story.
- Who's going to search tags for titles of individual fanfics? Except for a few particularly well-known ones like HP:MOR and My Immortal, nobody except the author is likely to be an expert on one specific fanfic. But someone might be very well-read in HP fanfic in general, and want to search the site for harry-potter fan-fiction questions to answer.
- It does usually require some knowledge of the original canon to answer questions about its fanfic. OK, HP:MOR is telling a different story from the real HP, but someone who doesn't care about HP won't care about MOR either. With many less-derivative fanfics, knowledge of the canon might even be enough to answer a question about the fanfic. By and large, it's our harry-potter users who're going to be answering questions about HP fanfic, so why not tag them accordingly?
No, they should not be tagged [harry-potter]
While Harry Potter and the Methods of Rationality is clearly a fan fiction that makes a lot of nods to Harry Potter, it is a very different story. It doesn't try to match the Harry Potter book canon at all. It's not like Cursed Child or the Sirius motorbike story JKR wrote, which tries to build on the books, although with at least some contradictions.
As a result, most questions about Methods of Rationality aren't Harry Potter questions at all, and they do not need Harry Potter domain experts. Thus, the harry-potter tag is useless on them.
Mind you, we do have three questions that ask about a comparison of Methods of Rationality and Harry Potter canon, and these three do need the tag:
- Can this HPMOR hypothesis be true in Harry Potter canon?
- Does the Interdict of Merlin appear in original Harry Potter canon?
- Does the world of Harry Potter and the Methods of Rationality differ in any other way from the original besides the husband of aunt Petunia?
But all the rest of the questions shouldn't have the tag.