It depends on how many specialist and generic roles you have.
More generic - Fluid/Very Fluid
More specialist - Rigid/Very Rigid
People saying base it off of your opponents and strategy are wrong (imo) you can play rigid/very rigid with an attacking system and vice versa with defensive and fluid.
The first thing you said isn't strictly true.
The specialist/generic roles thing is good as a general rule, but the terms 'specialist' and 'generic' are, in themselves, ambiguous. I know the 12 Step Guide roughly outlines which roles are generic and which are specialist, but you can't really take that as the final authority on the matter. For example, the Poacher could be considered a more 'generic' role than the Shadow Striker - whereas the guide indicates otherwise. Moreover, if the Winger, which generally serves one purpose (getting the ball forward and getting in a cross), is considered 'generic' by this guide then why isn't the Target Man?
What I'm saying is, the best way to understand Fluidity in game is to see that, in general,
it serves to increase the 'multi-functionality' of your players - a la Total Football. So yeah, the perceived 'specialist' roles do become increasingly obsolete with greater fluidity, but by the 'More Generic = More Fluid/More Specialist = More Rigid' logic this can still lead to confusions. For example, you may by coincidence have a first XI whose respective best roles may all be considered 'generic', but this does not mean you ought to play Very Fluid.
Sure, if your players are versatile with good mental stats, and you want to play a kind of football that revolves around unpredictability and positional interchange, then go ahead and play with fluidity. However, you may not have a squad cut out for that, and you might want to keep things simple by going with Rigid, even if you have your team set up in the alleged 'generic' roles.
However, even this cannot be interpreted as wholly definitive; as the guy on the last page pointed out, you can still have success with a lower-level squad playing with high fluidity. It just means that for best results proficiency in multi-functionality is advised. Of course, the other instructions you have set factor in to the efficiency of the fluidity level as well.
In general, higher fluidity does what it says on the tin: you can expect to see your players popping up in 'unexpected' positions more often, and your players "are expected to contribute to more than one phase of play" i.e. help out in all aspects of a match. You could, contrary to the logic in the post above, have a first XI made up of entirely 'specialist' roles and still play using Very Fluid, it just means those roles would become more of a rough guide than fixed job.
Hope that helped!