The pandemic is an exercise in trading rights for lives. More rights leads to more deaths and vice versa. You can make a case that society should choose any particular point on that spectrum but the spectrum exists regardless.

Because voter ids were used in the past for discriminatory reasons. Requiring vaccines to not wear a mask in a store is a huge false equivalency and typical of right wing rhetoric.

Here’s just one way: One inconvenience is designed to solve a statistically-proven massively widespread problem (community spread of COVID) whereas the other inconvenience is promised to solve a problem the statistics show is nearly non-existent.

You have to register to vote and link your vote to your registration.

The vaccine-card equivalent of Republican Voter ID requirements would be mandating that everyone present a vaccine card before being allowed to vote with the intent of discouraging eligible Republican voters.

The equivalent of present-day pollbooth security in vaccine-card form would be requiring people to associate themselves with an official vaccine record before shopping / working / etc. You wouldn't have to present an ID on the spot, but the records would be checked to look for two people claiming the same vaccination record, someone trying to claim a record that didn't exist, etc. Discrepancies would be investigated and if you were found to have fraudulently represented your vaccination status you'd be in trouble.

Well, in one case, we work very hard to try to get everyone vaccinated driving vans around with shots and doing everything we can to get shots in arms (and is free). In another case we have no problem telling people that the ID office within 100 miles is open the 5th Wednesday of months that have a 5th Wednesday (and is a "nominal" fee). Because in one case society benefits from everyone getting shots and in the other case the decision makers benefit from not everyone getting an ID.

That is to say, one major difference is the availability of the papers.