"nobody" in tag question

'Nobody' is always singular. Therefore, 'Nobody has...' is correct. It would take a singular pronoun, 'Has he.' That opens the he/she problem, though. I would rewrite the sentence to have a plural subject, which would use the non gender specific 'they'.

No people have disagreed, have they?

This is not very natural, though.

Another option puts it in passive voice.

There haven't been any disagreements, have there?

There hasn't been a disagreement, has there?

The simplest way is to ask the question without a preceeding statement.

Has anyone disagreed to the proposal?

At the risk of starting another grammar row, it should be noted that Nobody's disagreed with the latest proposals, have they? would be considered completely correct by great numbers of well-educated people.  The 'singular they' has been around for centuries, collocating with everyone, no one, etc., but so too has the grammatical controversy surrounding its use.

In a formal written context, I would tend to go with Lewis; however, in less formal spoken contexts, such as a tag question, use of the singular they is widespread and quite well accepted.