He has rare autoimmune disease which requires he be injected with gamma globulin once every 21 days.
Why do we use "be" in the sentence above? What does it mean?
Usually we wouldn't use "the base form of the verb" (be) in this position, but would use is instead.
Such use of be usually expresses a circumstance that is "desired, demanded, recommended, necessary, or similar" (according to Wikipedia). The construction of this type is known as "mandative subjunctive" (or "jussive subjunctive"). It's used with verbs like insist, suggest, demand, prefer.
He has a rare autoimmune disease, that's why he needs to be injected with gamma globulin once every 21 days.
The subjunctive is visible only when we use the third-person singular form of the verb.
Let's remodel the sentence, taking the third-person "nurse" as subject. Note the difference in meaning:
I insist that the nurse injects him with gamma globulin once every 21 days.
(I give my word that she does this. The "indicative" form, it indicates the reality or the speaker's view of reality.)
I insist that the nurse inject him with gamma globulin once every 21 days.
(I want the nurse to do this. The "subjunctive" form, it expresses a desired condition.)