Joseph
‘ is it the right of the government to deny entry where both parties (owner and patron) agree on permitting it?”
Yes. there is no “right of gym ownership” The government can not allow you to operate gym
We can think of many example where both parties agree on doing something yet the Government can prevent them. Certainly if said activities are deemed to pose a risk to public health
(That said I don’t think I agree with such a policy IF all involved are aware of the risks the gym should be allowed to operate , but as to whether the Government has the right to shut them down. certainly)