A study showed that if they wired two mice's circulatory systems together, one with Alzheimer's and one without, the second one would eventually develop everyone's favorite brain plaques.

https://www.newscientist.com/article/2151909-alzheimers-may-...

So while wiring together two bloodstreams is a bit extreme, and likely to result in most things being transmissible, there's nonzero evidence that you can have a bad day from a blood transfusion.