Vaccine's are a mix of different substances. Some of those are in the vaccine because they are helpful for achieving the sought after result, other's are there because they are a by-product of the production process.
Side-effects from past vaccines often were due to preservatives and adjuvants. Given that mRNA vaccines get stored at -70 C they don't need any preservatives. Adjuvants are also not needed for mRNA vaccines.
Old-fashioned vaccines are often bread in eggs. That means that the egg protein ovalbumin is included in the vaccine which can result in a patient developing an allergy against eggs. It's worth noting that most of the problematic food allergies in our society are not ovalbumin allergies or allergies against other food proteins that can be found in vaccines, so while this effect is undesireable it's also no reason to reject standard vaccines.
mRNA vaccines get produced by hela cells which are a cell line based on human cells and as a result there's less reason to expect food allergy development due to mRNA vaccines.
It's possible that the COVID spike protein has some negative side effects but if that is the case, not giving COVID-19 becomes more important which makes the vaccine more important.
The nanolipid coating that surrounds the mRNA and gets it into cells could have some interaction that leads to side-effects but as far as substances go it's fortunately not something that interacts much with biological processes.