Remember the days when every Google product was in beta? What happened? This labeling has fallen out of favor. My hunch: users don't care if a product is in beta. When is it ok to display the software release cycle to users?
I think it really depends on the release cycles of product updates and whether the releases are incremental or if a lot of changes are introduced at the same time.
Of course, people are now used to the idea of Google release updates constantly (and some just automate the process to apply the updates as well), but this obviously doesn't apply to every software company.
It seems logical that if small and frequently releases happen you don't want to annoy or flood the user with lots of updates and make them feel like the software is not stable (which a beta label is going to do). On the other hand, if large and infrequently releases happen you want to make sure that users are aware of the risk of an unstable or untested release and so it makes sense to do so in these scenarios.
"users don't care if a product is in beta"
Hmm not sure I agree there. I certainly prefer to know this when using any product, as I'll then adjust my expectations accordingly. Setting and meeting user expectations is generally a sound principle to follow. If I'm using a beta product, I'm not going to expect it to necessarily work perfectly. I might even be using it with a critical eye, and be ready/willing to report any bugs identified. If, however, I think the product is fully tested and validated, I'd be a little more annoyed and less understanding if I discover bugs while using the product.
Therefore, I'd say it's still OK to use the beta label. Just be clear around what "beta" in your context means, i.e., is it a technical beta or a marketing beta? And set user expectations accordingly.