Q:

In a unionized workplace, what does an effective method of conducting union discussions look like these days?

Back in the 1950's, when my grandfather was in his heyday as a labor organizer, the meeting at the union hall was a big thing. If there was going to be two-way communication between the leadership and the rank and file, that was probably where it would happen. Of course not everything was perfect. My grandfather told a story about announcing to his members that they'd negotiated a new contract under which wages would go up by 30 cents (per hour), and by the way, the union dues would go up by $2 (per month). He got a lot of angry feedback from members upset that the union was giving them 30 cents but taking away $2.
Today I'm a member of a public employees' union, and in-person membership meetings don't seem to be a thing. (There are meetings, but almost no  rank-and-file members attend.) We have the internet now. The structure in my union has basically been that the union president would get permission from management to broadcast emails to the membership (by sending mail to an address like allworkers@employer.gov, which would bounce if a typical worker tried to do it without the software permissions being set appropriately for that sender). As a rank-and-file member, I know and trust my shop steward, so any time I've had concerns, I've just talked to him, and he would talk to the leadership. Seemed to work fine.
But recently, some non-optimal features of this setup have become apparent. A  hot-button issue was decided by a relatively close vote in the rep council. Some people on the losing side of the vote were very upset. One of them scraped the addresses of all ~500 members off of the public directory, and sent out an angry email. Various people then hit reply-all and blew off steam, made accusations against each other, and made contradictory statements about facts. It's basically a perfect model of how not to run a constructive online discussion. The signal-to-noise ratio has approached zero. On the netiquette front, nobody opted in to the email list, and there is no effective way to opt out.
To some extent I think the union leadership was also to blame for this. During the decision-making process, they polled members about certain issues, but they didn't respond substantively to questions about these issues, so the members' feedback via polls was not informed feedback. There seems to have been a feeling that if there were a frank and detailed discussion, then management might be able to see it and use it against us. I guess this is the modern version of the old idea of management getting compliant workers to go to the union hall as spies and report back on what was said at the membership meeting.
Does anyone in a unionized workplace know of a better modern model for holding a civil discussion on things like this? Is there an internet-based model that works well? It seems awkward that the convenient IT resources are all controlled by management. Our local probably doesn't have resources to set up anything fancy, although maybe the state-level organization does. Maybe in a well-run union, the top-level union would provide a server with software, and the locals would use it...? God forbid that the whole thing be done on facebook.

A:

It seems awkward that the convenient IT resources are all controlled by management.

You are totally correct. If the union wants to be a "force", then it must not hand over some of its strengths to the "enemy".
In a better case, the union has its own IT "infrastructure", which will manage at least the following:

email communication;
discussions forum with polling capability;
document management;
members management;
assets management;
access rights management;
data back-up and restore (protection against failures);
ideally, redundancy;
internet access, of course.

By "management" I mean at least some text documents of any kind, holding information - not necessarily some complex dedicated software.

Does anyone in a unionized workplace know of a better modern model for holding a civil discussion on things like this?

As I already mentioned, a discussions forum with clear rules of communication should cover the needs. The polling capability of the forum software is mandatory. Meeting face-to-face might be better, provided that physical force will not be used in case of disagreement.

What IT infrastructure can be, is a totally different discussion. There are other places where to get that information from.

