Since this IS rhetorical, I'll pose a few more assumptions in the answer. To limit the number of potential answers, I'm assuming that the hypothetical management agrees with the employee solution. In other words, that employees and management have come down to a "yes, but we told the client..." impasse.
Reason for assumption: I can't in a single question handle the 1000s of ways out there of changing management's mind, all of which are influenced by a dizzying number of other conditions... so I'm assuming that employees and management are more or less in agreement, so this is just company/client
1 - Current contract?
The trickiest case is one where your company has a contract with the client. You'd think that particularly with respect to a gym or something similarly personal, that this wouldn't be common, but if you think about DoD contracting, where huge behavioral stuff can be declared in the contract, you could have some really annoying corrallaries that could be a contractual breach. For example a contract that says "site security monitors all entrances for working hours, 9-5 Mon-Fri" - then you could have a great deal of confusion when the conditions to change to "work hours are flexible - 7am-7pm, M-F". Now there could be an issue where the client contends you need to cover the door for 4 additional hours a day, which is going to be a huge cost.
I've seen worse.
These are going to have be ironed out on a case by case basis. Ideally, you can work out an update to the contract with the lawyers that doesn't cost anyone too much money. But this could be a dealbreaker and you may end up waiting out the contract. There are often very creative and cost effective solutions if both parties can agree, but it'll take creative negotiation to get there. It will always be a matter of making sure client concerns are represented with careful thought on the part of the company. And the realization that the client won't pay more just to change the scene for employees.
2 - Relationship, no contract
If this is a less formalized relationship, you may be able to approach it as a notification. If the relationship is one with high trust and low formality, you can likely notify them of a plan to change the policy, check in and get the customer concerns, address them, and move forward. It could be as simple as a phone call or a one on one email. The important part will be to make sure there's no change in in the quality of the work.
It's worth it to:
- notify and ask for comments
- notify of final plans and date of implementation
- check in over time on the client's perception of behavior.
3 - teams working together
Realize that sometimes it's a big deal when teams work together and culture shifts. It can be entirely within an organization where two sites work differently, or it can be between client and company where two teams work as one. Changing the benefits of one team can profoundly change another's satisfaction. Realize that small changes can have big impact and set norms that prevent the situation from decaying.
A big one I remember is that my last company had floating holidays while our customers had fixed holidays. From what I could tell, we stayed staffed up well enough that customers never noticed our holidays, but it was impossible to meet a customer deadline when all the points of contact took a fixed holiday. We had to be quite careful to plan schedules so that nothing was too close to a fixed holiday when approval would be required.
Even though both teams got the same basic number of days off, the way that they were taken was a big deal. With the gym example - if one site gets better gym privileges, they better be real clear that "oh, I was late cause I was in the gym" is an unacceptable excuse or the privilege will be revoked.