I feel like this is obviously fallacious, but I can't put my finger on it.

This meme is being used as an argument against employers, etc. requiring a covid vaccine card for their employees, etc. I realize there are other nuances, but I'm wondering about this particular argument.

"There are 800,000 registered sex offenders in the U.S. and they don't carry a card because it 'violates their privacy.'  Keep that in mind."

P1) People are required to show COVID-19 vaccination cards.

P2) Sex offenders, however, aren't required to show a 'card' (because it violates their privacy).

Implicit P) If sex offenders don't have to carry cards, why should regular citizens have to carry one?

C) People should not have to show COVID-19 vaccination cards.

Some issues here:

P2) is misleading. Sex offenders may not have to carry around cards, but their names are on a database that is often publicly accessible. They may be named in the media. Thus, their privacy is already compromised compared to a regular citizen. The meme is trying to say, "look! Those who committed sex crimes - a heinous thing - get to go free, while you have to show papers! This is unfair!", but it doesn't make sense when you think about what actually happens when convicted of sex crimes.

Implicit P) is misleading. Sex offenders may not have to carry around cards showing that they committed sex crimes...but convicts, on release, generally don't walk around carry cards indicating their crimes either. Thus, sex offenders aren't receiving any special treatment as implied in the meme. Also, everyone is required to show COVID-19 vaccination proof - whether a sex offender or not. So if someone did commit sex crimes, they'd still end up having to show some form of identification.

In any case, there is an enduring argument for COVID-19 vaccination cards that doesn't exist for 'sex offender cards'. COVID-19 is an infectious disease that vaccination can help to severely reduce the transmission, infection, hospitalisation and fatality rates of. This reduces cases, hospitalisations, and deaths. This helps society return to normal faster. Vaccination cards are intended to help nudge people towards vaccination, in order to expedite the process. Failing to consider that is a serious flaw in the argument.

So I'm not sure there are any formal fallacies, though there is an implied false equivalence between 'vaccine passports' and sex offender ID cards (you can't 'transmit' sex offender status).

There's boatload of ‘em: Reductio ad absurdum, strawman, appeal to extremes, false equivalence. Surely, carrying a card that proves you’ve been vaccinated is nowhere equivalent to being a registered sex offender. For one, the whole point of the registry is to independently expose one’s criminal propensities and predilections without relying on the perpetrators personal integrity.

There are lots of places to aim one's finger.

In part, it seems to be a false equivalence .  The implication is that providing evidence of having done something that protects society (having been vaccinated) is equivalent to providing evidence of being a potential danger to society (being a sex offender who repeats the offences).  The two cards serve completely different purposes.

Not to mention that there's already a public record (available to those who go to the effort of seeking it out) to indicate that one is a convicted sex offender.  There's no alternate public record of one's vaccination status.

There's also an appeal to emotion and argument by emotive language  from the selection of sex offenders as an example of some really bad folks who don't have cards to carry when we're making cards available to some really good people.

It's also probably a case of style over substance ... a neat sound bite is provided without evidence to support the conclusion ... in fact, what is the conclusion here?  I suspect it might be that we shouldn't be providing cards to demonstrate vaccination or that employers shouldn't be able to require production of such cards – but, it's not really clear if that's where the sound bite is going.

The implicit argument here is that requiring a vaccine card while not requiring that from a sex-offender, is a case of double standard . 

But claiming that it's either cards for everyone (sex-offenders and vaccinated people) or no cards at all, is a case of False Dichotomy.