The recent Civil War movie had the president serving a 3rd term leading to 19 states seceding. How would the blue states respond to Trump ignoring the 22nd amendment?

The same way they responded to ignoring of the 14th? The Supreme court will provide some travesty justification and that'll be it.

As a general rule, with some exceptions of course, Democrat politicians tend to "roll over and take it". If the Supreme Court rules that Trump is the president from 2028-2032, expect blue state leaders to just go "oh ok" and then accept that he is the president.

You can contrast it with what red states would do if Obama had a third term.