The ref tag is not just for navigation. There is no consensus for removing all of these ref tags.

You must discuss BEFORE making bulk changes. It is not much of a discussion if you just ignore anyone that disagrees with you anyway.

Please stop your automated edits, which there is no community consensus for.

Have you read the automated edits code of conduct? osm.wiki/Automated_Edits_code_of_conduct
You have failed to document what you are doing. You have not discussed it beforehand. You have not used meaningful changeset comments.

You are not complying with the Automated edits code of conduct. There is no consensus for these bulk changes.

The list of U class roads contains plenty of errors, and road names that don't actually exist, or are out of date. I wouldn't assume it is correct.
It is useful if it is flagged as an error, because then you know it needs surveying, to check what the name actually is. It is not helpful if you hide these errors by adding not:name tags for everything.

What does it say on the sign? How do you know it is an error in the OS data?

Why did you remove the addr:interpolation as unneeded? These are buildings with multiple housenumbers. So how to tag that the address is a range of numbers, either odd, even, or all numbers.
See the wiki, which suggests using interpolation tags (though says there is no consensus). osm.wiki/Addresses#Buildings_with_multiple_house_numbers

The main restriction for cars is you won't be allowed on the ferry unless you have a permit. Same as for Eigg, Muck, Canna or Knoydart. For people living and working on the island, it is used as a public road.
The road on Eigg is officially designated as an unclassified road (with a prohibition order on vehicles), the only real difference is it is adopted and maintained by Highland Council.

The tag highway=unclassified is usually used for roads owned and maintained by the local authority, but I think there can be exceptions.

I believe it is currently maintained by SNH, but is to be taken over by the Isle of Rum Community Trust sometime soon. Anyway, I think it is important as the only main road on the island, connecting the ferry to the village and all of the amenities. And it is effectively a public road. So tagging it as unclassified makes sense.

What sources are you using for these changes?

Wrong comment, from previous changeset. Should say Kiltarlity - new streets

You have mapped several forest tracks as highway=unclassified. These should be tagged as highway=track. The 'unclassified' tag is only for minor public roads.