Normally, no.

You’d have to set up a completely new account which you only ever access via e.g. Tor, then use Tor Browser on iOS to log into that account and only ever use your account exactly like this or else you’ll leak your current IP address as well as related data about you or your device to Meta. Also you’d have to never give any kind of personally-identifiable info to them. Then you’d have an anonymous account, but the goal of Facebook is to connect to other people you know. Once you add and talk to friends on Facebook, they again know who’s behind that account, especially if you already had a different account in the past which pretty much had the same set of friends already. So you’d also have to behave anonymously when using your anonymous account. Which kind of goes against the whole thing of social media like Facebook. So yes it’s possible, but inconvenient, and maybe even counters your goals on that platform. Which is why I recommend to not use such platforms at all, and instead keep in touch with your friends via secure and private open source based messengers like Signal or Threema (Libre?) or any Matrix client.

Using Facebook in any other way, shape or form isn’t going to be anonymous to Meta. They’ll automatically receive your current IP address (which might already be enough to be probably personally-identifiable for them, since they also have trackers in place in lots of other apps and websites), and on top of that various information about your device or browser (which, again, can be a key factor to link your current usage data to your person), if you use their app (which you shouldn’t ever do) they get even more data on you (not just you, also your contact list, nearby devices, and things like that), because those apps require so many permissions and have so much tracking integrated that it’s a whole treasure trove of information that’s being sent about you and your device, and they’ll interconnect all that data with the other data they’ve gathered about you or your device(s) in the past (which, as a rule of thumb, will always be much more than you think they’d have). An app with integrated tracking is always more harmful to your privacy than using their service from within a web browser, because the app can read much more data about your device compared to the web browser. (But be mindful that some web browsers (especially the proprietary ones like Chrome, Edge and Opera) also have quite a lot of tracking capabilities inside them.) So using Facebook in a somewhat normal or convenient way and at the same time wanting to remain anonymous to them is basically impossible.

Also, you’ll never be anonymous to government-based mass surveillance (who are collecting almost all network traffic, constantly) when you use your real IP address online. Anywhere. Your real IP is always connectable to your real person for them (also in retrospect). Even if they can’t look into encrypted communication data, like the contents of chat messages or what you did on a specific website, they can see the metadata, among that is which hosts you contacted, and when, as well as more unencrypted details, and such metadata can already be very revealing. To quote the ex NSA chief “we kill based on metadata”. Protecting yourself against commercial-based surveillance by companies like Meta is more realistic to achive (at least partially), because it’s easier to avoid or evade commercial tracking (by blocking all or most of their tracking methods like app-integrated trackers, tracking Javascripts and cookies on countless of websites, and so on) than it is to evade someone who’s sitting directly at all relevant network cables AND buys additional data from companies. Lots of easy-to-use tools exist to counter or limit commercial surveillance, like ad/content blockers, blocking host lists, PiHole, ad-blocking DNS servers, open source software and operating systems (because they are almost always free of trackers and surveillance tech), and things like that. It all minimizes your exposure to these data hoarding companies. And the less data you transmit overall to such companies, the better. But if you also want to protect yourself against any government-based mass surveillance, you’ll have a much harder time than that. You’d need to always use different IP addresses (again, via Tor or VPN etc.) and avoid having anything leak out that can connect your other IP to your real IP. Which is hard.