My understanding is that services like this use some authorized device to send and receive iMessages for a number of users, and then those messages are relayed elsewhere. Services like this have existed for those with Mac workstation at home (or a Mac otherwise persistently connected to the internet) for a number of years. I guess Sunbird is different by eliminating the requirement that users own a Mac.
I highly doubt they're interfacing with the iMessage backend directly — if they were I'd figure they could at least get read receipts working — but instead they're probably using AWS or MacStadium or similar to spin up a bunch of Mac user accounts in the cloud, each of which is both able and allowed to access iMessage. At that point, it's just a matter of syncing ~/Library/Messages/chat.db.
Not only is that not illegal, but also I'm not seeing how it even violates Apple's terms of service or EULAs at this time. Apple could, of course, update their terms/agreements to forbid this practice, and they could also implement workarounds in macOS to make services like this more difficult. However, even if it were to be forbidden by their terms/agreements, the practice still wouldn't be illegal in and of itself. EULAs are not laws.