I have that option, but if I use my phone with Wifi disconnected, I'm able to get past that. Then I go back to my PC and complete the rest. Another couple of options:
1 - Contact the host of the comp and ask if they can whitelist your e-mail address
2 - It goes against the suggestions sweepwidget makes, but if you have a VPN (or even free VPN), try connecting it and trying again. I think IP address might have something to play in the check also.
Failing that, DM me a name and e-mail address and I can start off the entry for you. Then you can enter those details again at your end and finish the comp entry.
Sucks that I cannot enter literally any competition on sweepwidget due to the stupid anti-spam system