Yes, leuprolide chemotherapy (Firmagon, Lupron, Eligard) impairs immune system function such that it cannot stop Shingles outbreaks.
I got Zostavax before going on the first round of Eligard, but got the nasty, bloody belt around my middle anyways. That lasted months and left me with that burning nerve damage (neuralgia). Before I went back on leuprolide chemo the second time I got the 2 Shingrix shots 3 months apart. A week or so after the first leuprolide chemo injection last Nov I got a Shingles outbreak on the back of my calves. Wasn't as bad as the first round though, but was still rough. Gratefully that has faded away. Since the Xtandi also comes with warnings of a compromised immune system I hope not to get Shingles back and am trying my very best not to pick op C-19. Also got the pneumonia shots, still need to get the whooping cough shot.
Reminder: we here are an "at risk" group. 'ADT' is chemotherapy and has some serious side effects regardless of the marketing PR.