Where are you getting the message that a firewall is blocking you? If it comes from your firewall itself, then you can simply configure your firewall.

To play games all you should really need to do is make sure the firewall allows outgoing TCP connections by all of the BYOND programs, and the pager (byone.exe) should also allow incoming TCP connections. You'll also want incoming connections allowed for dreamseeker.exe and dreamdaemon.exe if you ever plan on hosting a game, so it's probably easiest to give them all full access.

In your firewall settings, make sure that if there's a setting to keep a hash (e.g., MD5, SHA, etc.) of the .exe to make sure it hasn't changed, that you disable that setting. The reason that needs to be disabled is that on some firewalls, they don't respond properly after a BYOND update and then suddenly all of the programs have trouble communicating.

Keep in mind many antivirus programs also have firewalls of their own. Your antivirus may have a similar list of prorgrams it will and will not allow to use the Internet.