Sheikh Abu Esa of Al Maghrib Institute clearly breaks down the issue of gelatine in vaccines in general and in light of the Covid pandemic.
Is there Gelatine in the Covid Vaccine?
Pork products being part of their vaccines has been ruled out by Pfizer, Moderna and AstraZeneca – it is not yet clear if other vaccines in the market are gelatine-free
Why is Gelatine Used in Some Vaccines
Porcine gelatine is used in vaccines as a stabiliser – to ensure that the vaccine remains safe and effective during storage... the product used in vaccines is highly purified and broken down into very small molecules called peptides.
Source: https://www.swlondon.nhs.uk/vaccines-and-porcine-gelatine/
What Do Other Authorities Say?
Vaccines containing porcine are not permitted in Islam unless lives are at risk and there are no alternatives.
Souce: https://mcb.org.uk/mcb-updates/position-on-flu-vaccines/