While it only takes two thirds of the states to call for a constitutional convention, under Article V three fourths of the states (presently 38 of 50) is the minimum necessary to ratify.
So, we only need 13 states to reject any new Constitution or Amendments. Well, let's suppose that the new document takes away gun rights. In that case, the following states at a minimum could be counted on to reject it:
Alabama
Alaska
Arkansas
Florida
Georgia
Idaho
Kentucky
Louisiana
Mississippi
Missouri
Montana
North Carolina
North Dakota
Oklahoma
South Carolina
South Dakota
Tennessee
Texas
Utah
West Virginia
Wyoming
That's 21 states, and I didn't even include some that I think would go our way.
If there's a Con Con, there is danger, but it would be a danger of incrementalist crap. The more pressing danger is either more incrementalism or a "Reichstag Fire" scenario.