I didn't know this was possible, but apparently you can now use Signal anonymously.
This is enabled by using publicly available phone numbers together with a new "Registration Lock" feature which prevents re-registering such a phone number (since users don't own them) and thereby stealing the account.
https://community.signalusers.org/t/how-to-use-signal-anonymously/2277
@jeroenpraat As far as I understand the procedure, you don't need to be in the US or Canada. You will get a US or Canada phone number to use for Signal, yes, but that doesn't matter at all. It's just a random number.