Do vaccines conflict with my religion (for example pork gelatin)?
Here is what the checked sources say. Each title links to the original.
Religious exception for vaccination or religious excuses for avoiding vaccination
A 2016 review by authors from several countries of what Catholicism, Orthodoxy, Protestantism, Judaism, Islam, Buddhism and Japanese folk religion teach; the authors note it does not cover all religions. Catholic guidance it cites says vaccines from old fetal cell lines should be avoided where alternatives exist, but are morally acceptable when none is available. Islamic scholars it cites permit pork gelatin under the law of necessity, because vaccines are medicine, not food. The authors argue these traditions' core teachings do not oppose vaccination, though some believers and leaders interpret them otherwise.
Vaccines and porcine gelatine
This UK government leaflet explains that some vaccines use highly purified pig gelatine, broken into tiny peptides, as a stabiliser. In the UK it is in the nasal flu spray, MMR VaxPro and ProQuad. Gelatine-free options exist: Priorix for MMR, Priorix Tetra for MMRV, and an injected flu vaccine. A Jewish dietary-law service told UK officials that animal ingredients in non-oral products, including vaccines, pose no problem. Views vary within Muslim and Jewish communities. Brand availability differs by country.
Note on the morality of using some anti-Covid-19 vaccines
The Vatican's doctrinal office said in December 2020 that when ethically unproblematic COVID-19 vaccines are not available, it is "morally acceptable" to receive ones developed or tested using cell lines from past abortions, because any cooperation with abortion is remote. It said vaccination is generally not a moral obligation and must be voluntary, but that the common good may call for it, and those who decline should take other steps to avoid spreading infection.