I can no longer create a new one without using an email tied to my identity

I haven't bothered to look into it, but historically, there were a lot of sites that let one create throwaway email addresses to avoid handing over email addresses and tying an online handle to personal information.

Sites that harvested this email data fought back by trying to blacklist those "throwaway email address" sites, but it's a game of whack-a-mole—like, those throwaway email address sites also set up and discard domains from a pool—so I imagine that it's likely possible to manage to find one that works, if you're determined to do so.

Note that throwaway sites do create security issues in that password recovery and similar often relies on a registered email address, so you're potentially entrusting some random throwaway email site with access to your account, since it can receive email from the site. I wouldn't use that for something important, but depending upon use, it could be useful.

Also, a number of sites—I don't know about what Reddit will be doing, but I think that Google requires this for account registration these days—require a phone number, and at least in the US, while you can get VoIP SIP service, don't need to tie that to a phone, I understand that there have been legal restrictions added on SMS service from this crowd in the past few years. I don't know if Google permits for validating a phone number via voice or requires demonstrating SMS capability.