Don't know about Broadway, but every West End Show allows you to take alcoholic drinks into the Theatre. We have been on QM2 twice and took drinks into theatre with no complaints as we have done on many other cruise lines.
We are also on 7th Oct sailing, however we will be in US for 3 weeks before joining Queen Mary, the last 5 days in NY, so will wait to the last minute before booking covid test as things may well change by then.