And Switzerland was famously neutral until it wasn’t.

There are no rules.

NATO 'can' do anything it wants, of course, because there's no judicial body to invalidate it if they do admit a member with unresolved border disputes. That said, they are smart enough (and 'not crazy' enough) to abide by that.

NATO can't accept an applicant country that is at war or has any unresolved border disputes

NATO can accept any country as long as it has consent of the current members. There are no rules or criteria other than that. As long as all the countries agree, anyone can join at any time:

This is a common misconception that has its roots in the 1995 Study on NATO Enlargement carried out by the Alliance. A closer reading of this document shows that a territorial dispute does not necessarily prevent a country from joining the Alliance. Here is what the study says on the matter:

“States which have ethnic disputes or external territorial disputes, including irredentist claims, or internal jurisdictional disputes must settle those disputes by peaceful means in accordance with OSCE principles. Resolution of such disputes would be a factor in determining whether to invite a state to join the Alliance.” NATO (North Atlantic Treaty Organization), “Study on NATO Enlargement,” last updated November 5, 2008