No, you can't totally separate the arguments from groups, because people personally identify with opinions, and assign opinions to groups. But you can separate the idea from the people that say it — "I agree with this because Stephen Hawking said it". The disassociation just means you have to engage with the idea rather than accepting it based on who made the argument.
This is fine if you don't want to change your mind, but at any rate, seeing the debate laid out forces you to engage with it. For the gun debate, for example you might see "permitting gun ownership leads to much higher rates of homicide". The first gut reaction would be to say "That's just not true!", which motivates the reader to click on that argument and argue against it… leading to further engagement. Debate is the one place we actually are naturally motivated to see the other side, if only to disprove it!
And that's the main point: Facebook and Twitter create bubbles and drive us apart. Organized debate naturally interlaces opinions, and can have the opposite effect.