//Is it any more Nazi than requiring passports or certain vaccinations to travel to /from certain countries, DBS checks for certain jobs, having to prove qualifications,etc.//
Yes it is. The activities you mention are traditionally those that need the documentation you mention. Going to the theatre or pub does not. What is proposed is restricting people’s movements on the basis of the medical treatment they may or may not have undergone. Apart from that, the scheme is ridiculous. Those vaccinated can still pass on the virus. All a “passport” is doing is allowing large numbers of people to congregate with legitimacy, but not with any greater safety.
//Its just to go to certain risky events for a certain period as a precaution. Its only going to far if you cant go shopping or leave the house without one//
“Temporary” measures have an alarming habit of becoming permanent (example: Advance Passenger Information for international travel). Why is it going too far to impose it to go shopping, but not too far if you want to go to a pub or restaurant? What makes you think it will not be imposed for those activities anyway? Have you heard of “salami” tactics, or “mission creep”?
This country is tumbling towards becoming an authoritarian, dictatorial state where people’s liberties and freedoms are being summarily withdrawn on a whim as soon as there is a threat of the NHS coming under stress. As you've demonstrated, it is being accepted with alarming readiness.