Reddit reviews Immunologic Disorders in Infants and Children

late reply and others covered the main issues but one more to highlight:

IgA deficiency in humans has more than one cause. In some people, it seems that for some reason B cells are incapable of class switching to IgA. However, in others the low IgA levels are actually due to an immune response against IgA. Basically an autoimmunity targeting IgA molecules, which effectively clears IgA from the body. In the former cases, a transfusion wouldn't cause many problems but wouldn't do much either (other comments mention reasons for this). In the latter case, a massive immune response directed against the transfused IgA can occur and cause acute and very serious health problems. In fact, IgA deficient humans are screened during provision of some types of donation (e.g. IVIG source) because the donor's anti-IgA antibodies will cause inflammation in the [most likely IgA-sufficient] recipient.

this old book provides more detail on what I've written: https://www.amazon.com/gp/product/0721649483/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1

I can go dig up the primaries if needed; here is an abbreviated version of what is in that textbook: https://link.springer.com/content/pdf/10.1023%2FA%3A1012241117984.pdf