No, actually, MR specifically accounts for these variations.
However, one idea (one that would need a lot of evidence in my opinion, but to give you a clearer picture) that is not captured by MR is horizontal pleiotropy. So, if the genetic variants used in this study e.g. actually cause someone to seek out dietary modifications/solar augmentation of vitamin D, that would not be accounted for here.
I don't think the biology in this case allows for that to any significant degree, but I'm not an expert in vitamin D metabolism/action or COVID.
> I don't think it's an honest assessment
The title here is maybe a bit simplified, but the paper is quite honest about its weaknesses if you read it in its entirety.