I fail to see how banning guns makes people freer.
IIRC, nobody made such claim.
That's the entire purpose of having a republic.
The purpose of a republic is that you don't have a monarch. Which isn't what these polls were about either...
Strange. I used to think that the purpose of a 'Res Publica' was to make issues 'Public Things', than an overpowered individual could not enforce one's sole desires and auspitions over the others, owning and controlling everything under one's power on the process. Clearly, this will make some people freer (those who control the public issues). Sure, not having a monarch (and aristocrats) that sees the State (and obviously it's gentry) as his/her property is a really good beginning.
In a democracy, citizens control those issues and, when you restrict that control (or disenfranchise citizenship, somehow), then you're putting degrees of autoritharianism. But not of non-republican system. Yet, you can have democracies with non-republican aspects, if you let private interests pass over the public ones. The main issue is on what is a public interest, what is not, and how is the interaction between a putative public interest, a private interest, and the various shades of interests of partial groups. That's why republics always have assemblies and selfcorrecting law systems.
But I can't see too much conceptual differences between modern parliamentarian monarchic democracies and republican democracies, except the formers having an extremely expensive kind of public servant.
Gun banning, on the other hand, can result in a pretty public benefit, but I wouldn't make an issue over this. A responsible armed population may also be.