Sync is charging for an ad free experience and/or extra features in order to fund the app's upkeep and because the app is the dev's source of income. People are torn about this because other apps are free, but generally aren't as polished and don't offer as many features, plus the sync dev has a good reputation and a long history of appreciated work. They also charged for similar stuff on their reddit app, but it was significantly cheaper. The prices seem experimental based on community feedback, so they may be subject to change, but some people see any pricing as a bad thing no matter what, while other people are in favour of supporting the dev even at the current prices. So far personally I like sync the best out of every app I've tried, and it is very similar to their reddit app which I used exclusively, but I also haven't seen any ads like other people say they've seen, no idea why, so my own experience is coloured by that. That's the issue regarding the free part at least. In terms of open source, it was made by one dev iirc, or at least has a small dev team, so it isn't open source. But closed source isn't automatically bad, people have just sorta gotten a bit open-source obsessed on lemmy and some people act like anything that isn't open source is evil. The main issue is the pricing stuff with most people though.
The problem isn't that it's paid.
There is nothing wrong with paid software.
The 'free' in 'Free and Open Source Software' is for Freedom, not for zero cost.
The problem many people on Lemmy have with sync is that it's proprietary/closed source and loaded with trackers and ads, relying on a subscription model to remove things that should not be there to begin with.
This business model of collecting and selling user data is considered extremely unethical by many, including myself.
I, and other free software advocates, also have a problem with shutting users off from viewing, accessing, and modifying the code that runs on their own devices.
Lemmy was built on the principals of software freedom, and many of us were attracted here for precisely those reasons.
Many of us see proprietary adware apps such as sync to be unethical, and are especially uncomfortable with them being used on top of Lemmy since we view them as being antithetical to principals upon which Lemmy was founded.
As an open source enthusiast, it was quite exciting to see a truly free/libre platform gain popular traction, and then extremely disheartening to see how quickly so many users would squander their new found digital freedom for a few minor conveniences.