I don't think liberal democracies care about these freedoms, other than as a rhetorical stick to hit countries that "illiberal" with. E.g. imprisonment of Julian Assange, removal of Trump from twitter, Atlantic Council as official part of FB content moderation team (w/ the probably-not-coincidental) subsequent removal of pro-Venezuela and far left groups.
(Plus also IMO being banned from FB and Twitter are materially much more harmful to a political movement than being banned from an app store. EDIT: Maybe not, since per other comment it was being used to organize election results.)
Yes, I agree there is much hypocrisy amongst those in power regarding this issue, and liberal democracies as such do not "care" about freedoms.
But then, why do they have laws punishing corruption in a foreign country? And why do they care if one of their citizens travels to a foreign country and performs a sexual act which, while not technically a crime at the current location, would be a crime back home?
Whether the motivation of these rules is purely utilitarian ("We don't want our businesses to get good at corruption, in case they start bringing it back" or "It's easier to catch active paedophiles having this option"), honestly moral ("Corruption/sex tourism is a scourge for developing countries, we must do anything to stop it") or even cynically electoral ("Let's look tough on crime to win votes"), any of these three options could be applied to a law against collaboration with repressive regimes.
In particular, given the dependence of our economies on the likes of Alphabet, Apple, Facebook, etc. and the increased power of China, I think that the utilitarian motivation should be enough. We don't want businesses that are so entrenched in our day-to-day to be so cozy with repressive authoritarian regimes which may sooner than later start to apply their own requirements on how businesses should operate in other countries if they want to have access to their own lucrative market.
If I were to hazard cynical guesses, I'd say anti-corruption drives are genuine, in that corruption hurts American business interests, and anti-sex-crimes stuff is convenient to intelligence services who use sexual transgressions as black mail (e.g. Alexander Acosta explaining why he cut a sweet-heart deal for Epstein: "I was told Epstein 'belonged to intelligence' and to leave it alone").
(Plus also IMO being banned from FB and Twitter are materially much more harmful to a political movement than being banned from an app store. EDIT: Maybe not, since per other comment it was being used to organize election results.)