Also advocate IV IgG soon

I hope your husband is doing better and that the infection is under control.
I have a couple of suggestions. I work with children with autoimmune diseases at my hospital. When we use Imuran, we watch the WBC pretty closely so that it does not get too low and cause a significant risk of infection. We ofter target an absolute lymphocyte count of 1000. The absolute lymphocyte count is the WBC X 10 X the number of WBC per hundred cells. So, if you husband’s WBC was 1.9 and he had 10% lymphocytes, his absolute lymphocyte count would be 1.9 X 10 X 10= 190. If someone is really low, they are more at risk of infections for which immunoglobulins help with the resolution–this can include sinus infections (which IgA helps to resolve) and viral stomach flus. Your husband was either on a dose which was too high or he is especially sensitive to this medicine (which has the same general effect).
2. Absolutely you do not need to stop the prednisone before starting IV IgG. I think the neurologist may have said this because it both are used it is hard to know which is helping and if both are really needed. Your husband is, however, not doing well with CIDP control on the prednisone and imuran and he is getting toxicity including infections severe enough to require hospitalization. This is an indication that sometime needs to be done differently and soon. They may want him to be stable from the infection before the IV IgG (meaning no fevers and no low blood pressure concerns) before giving the IV IgG, but he does not need to wait very long. Depending on which antibiotic he is on and his kidney status, it might be important to make sure there is plenty of fluids going through the kidneys to make urine before the IV IgG.
Added in edit. I meant to also say that the above is that “you do not need to stop prednione”, but there is a “you do not want to stop prednisone” part too. You want to keep control of the disease and if they try to taper completely off prednisone first, this is unlikely to happen. In a perfect world, you could use just one, but bad diseases require imperfect methods sometimes. They can use both IV IgG and taper slowly off the prednisone and see if your husband can be okay with only this treatment. Some people need both, but also some people do better with pulse steroids than with daily doses.
3. IV IgG at this time may help not only the CIDP, but also help ward off infections.
Many people on this forum have gotten IV IgG for GBS/CIDP including me and it helps.
WithHope for cure of these diseases and to make it safely through the treatments until that time.