I have a UK passport and a New Zealand passport. Assuming UK is no longer part of the EU, and UK passport holders are allowed visa-free visits to the Schengen Area for 90 in 180 days just like NZ passport holders, can I enter, say Spain, on my NZ passport, stay for 90 days, leave for a day, then re-enter on my UK passport for another 90 days? Therefore basically living in Europe permanently while not exceeding the 90-in-180 limit on either passport? Since I would technically be a tourist, I could, therefore, maintain tax residency (and my job) in the UK?
You, as the national of a visa-exempt country, may visit the Schengen Area for up to 90 days per 180-day period. Whether you hold more the one passport from the same country (it is legal in some situations) or hold passports from more than one country is irrelevant. You would still be the same person.