There is no evidence to suggest that people with coeliac disease are at higher risk of contracting COVID-19 or at higher risk of serious illness related to COVID-19 infection. Therefore, it is unlikely that having coeliac disease will place you in a higher priority group for COVID-19 vaccination. Discuss any individual health concerns or risk factors with your doctor.
The official covid19 government information is available on this link https://covid19.govt.nz/health-and-wellbeing/covid-19-vaccines/#our-covid-19-vaccine-strategy
There is also good information on this site https://www.immune.org.nz/covid-19-vaccines
The definitive message about safety comes from the immune.org.nz site.
“COVID-19 vaccines are being held to the same safety standards as all vaccines. New Zealand will not be approving COVID-19 vaccines for use until they have reviewed sufficient data on both safety and on how well the vaccine works (efficacy). Internationally, tens of thousands of participants were enrolled in each Phase 3 trial and mass vaccination campaigns involving millions of people are currently underway. Safety information on those who have been vaccinated is being closely monitored. All clinical trials involved an independent safety monitoring committee. These vaccines may have been produced quickly however we can be confident that no shortcuts with regards to safety have been taken”