We should respect other people's time off if we want others to respect our time off. Is it really so hard to find some other way to exercise for a month?
Why not close supermarkets out of respect for labor unions as well, for 2 weeks. I think the solution lies somewhere else - such as automating humans out of retail and services to the extent possible. For instance, speaking of gym, I would keep the facility open staffed just with with security and reception. Shut down non-core functions: new member office, group sessions, cafe etc.