Many people argue that vaccine passports will lower the spread of covid however the problem with their argument is that even you are vaccinated, it doesn't mean you can't get covid, it just means you are less likely get a severe case of covid that's likely to put you in hospital. You can still unknowingly carry the virus and infect others. According to a study from the CDC, 74% of people infected in a covid outbreak in Massachusetts were fully vaccinated: https://www.cnbc.com/2021/07/30/cdc-study-shows-74percent-of-people-infected-in-massachusetts-covid-outbreak-were-fully-vaccinated.html
Another drawback of vaccine passports is that such a system disproportionality affects people in immigrant and ethnic minority communities. Black Lives Matter New York slams Mayor Bill de Blasio's vaccine mandate as "racist and disrespectful": https://www.blackenterprise.com/leader-of-black-lives-matter-new-york-chapter-calls-vaccine-mandates-racist-and-disrespectful/