This is not illogical at all. While I appreciate your worries, YABU.
There is a tiny theoretical risk that any of us could be carrying vCJD.
We may be able to pass this on in our blood and breastmilk (again this is all pretty theoretical).
There is currently no test for vCJD in the blood.
The vanishingly tiny risk of passing on vCJD in breastmilk is completely outweighed by the massive known benefits to mother and baby of breastfeeding.
If you have been given a blood transfusion (a procedure which is never done lightly), there is a theoretical risk that your risk of vCJD is higher.
There is still no test for vCJD.
As the risk is (very slightly) higher and other breastmilk donors are available, it is better to give these very tiny and very sick babies milk from the lowest risk (there is no such thing as a no risk) donor.
In the same way, here in the UK, we advise mothers with HIV not to breastfeed as there is a tiny risk that they could transmit the virus by their breastmilk. In developing countries, however, women with HIV are advised to breastfeed because the risks of transmitting HIV are outweighed by the real risks of using formula where there is no clean water.
There is another concern about vCJD. When they do develop a test for it, all blood donors will need to be screened and then refused if they have a positive blood test. Being a child of the eighties, I think it is impossible that I didn't eat contaminated meat and so must have been put at risk. As yet, there is no treatment or benefit to knowing your blood test is positive for it (or indeed no way of knowing just how many people will actually develop it who have a positive blood test), so I don't want to know the result of my blood test, so I will end up stopping giving blood, I think.