Vitamin D and Immune System

[teo123]

When I told my father I want to be a vegetarian 5 years ago, he told me he is concerned my immune system might become weaker due to lower Vitamin D levels (as he has read some studies from 1930s blaming Vitamin D deficiency for the epidemic of tuberculosis in Croatia). Back then, I interpreted it as complete gibberish because, first of all, Vitamin D has, as far as I know, nothing to do with the immune system.
However, now newspapers keep telling us Vitamin D can boost our immune system and fight coronavirus. So, is there something to that? Is there a scientific explanation of how Vitamin D can boost our immune system? If there is not one, then it is most likely gibberish, right?
I've heard some people suggesting a rise in vegetarianism is responsible for the pandemic, because vegetarians are supposedly more likely to be deficient in Vitamin D. This is supposedly because they have lower HDL cholesterol, which is necessary for synthesizing Vitamin D. I am unaware of any studies suggesting that. Some people are saying eggs are the solution because of the cholesterol in them, but, as far as I understand it, cholesterol you eat has no effect on the HDL cholesterol in your blood, it only adds a small (probably insignificant) amount of oxidised cholesterol into your blood. As far as I understand it, the best way to raise your HDL is to eat more omega-3 acids.
Many people are suggesting supplementing with Vitamin D. I am not sure what to think about it. While you can argue that the evidence that calcium causes heart attacks is too weak, as far as I understand it, the evidence that Vitamin D causes heart attacks is not nearly as weak. So, there is a risk involved with supplementing with Vitamin D. And given that the benefit of boosting your immune system with Vitamin D is wild speculation, it is not worth that risk, right?

[teo123]

What, nobody is interested in this? I thought this is what this forum is primarily about.