I am sure you have all tried to do some research on this issue, and found as I did, an absence of guidance. So I turned to my trusty VAERS database. With about 500,000 reports of adverse events out of 340,000,000 vaccinations, if there's a problem, it's going to show up there. So there were 7 reports of reactions POSSIBLY linked to MTHFR, including 3 hospitalizations and 0 deaths. Since as many as 30-40% of the population has the C677T mutation, it is reasonable to surmise that a lot of people with MTHFR have been vaccinated, so it looks like a very rare side effect.

In contrast, a number of severe Covid cases, including hospitalizations have been linked to the mutation in some groups, see: https://onlinelibrary.wiley.com/doi/10.1002/jcla.23798 According to the article, the gene, and a specific mutation (C677T) they cite, can actually predict a higher chance of severe Covid infection.

In this case, absent other health issues, or medical advice to avoid vaccination, it looks like vaccination is a safer choice than a chance of infection...but only you and your daughter can decide.

Sue