What I don't get is how they would tyrannically enforce the gender restrictions or the union restrictions, in cases where violating them would lead to greater profit.
We need to get Sci in here, he would explain it quite well.
In addition to the FCA acting like just another bullying corporation, the FCA functions to protect the ultra-capitalist system
. The existence of unions in particular is a threat to those who have power. Unions get better wages and working conditions for the workers which diverts money and power away from the business owner. This dynamic is as true in the Ferengi Alliance as it is in our world today.
It's also similar to why the US government is/was obsessed with the domino theory. If one country is able to go its own way independent of what Washington wants, then it can encourage other countries. It becomes the "threat of a good example." Similarly, if workers at Quark's unionize, other workers will see that it can be done and agitate for their own unions. Squash the union at Quark's and it helps prevent other unions too.