After reading:

Where to have discussions about intuition?

It's pretty explicit that the main Q&A site isn't for gathering opinions or general extended discussion about math/math related topics (ex: "Has anyone else had issues with textbook X, I don't like the style, is it just me?")

Are these fair game for the math chatroom, (assuming someone else is receptive and you're not filling up space talking to yourself).

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    $\begingroup$ I should hope so. The big problem with "opinionated questions" is that they can drag on, and the chat room is better suited for that. That and the content is also out of sight if it turns out it was trolling. $\endgroup$ – rschwieb Mar 22 '16 at 10:46
  • $\begingroup$ "Can the chat be used to discuss opinionated questions?" Better to say: should it be used for this purpose? $\endgroup$ – goblin GONE Mar 24 '16 at 5:35

Yes, that's perfectly fine. Since you have more than 100 rep points you can even create a chat room for your discussion, if you're afraid of filling up the space of the main chatroom. To quote the help center:

When should I visit chat?

  • for real time collaboration
  • to meet the fellow members of your community in a more social environment
  • for less structured, casual (but still roughly on-topic) conversation

Honestly, even if it wasn't on-topic, the harm done would be so minimal that I wouldn't fret over it. As long as you're not flinging insults or discussing horrible things, it seems to me you can talk about pretty much anything you want.

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    $\begingroup$ I haven't been in chat in a while, but I can corroborate that "you can talk about pretty much anything you want." $\endgroup$ – pjs36 Mar 22 '16 at 18:33
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    $\begingroup$ To quote part of the tagline: "rarely expressible as a ratio of two integers.", So, almost anything within reason can actually be discussed in there. $\endgroup$ – J. M. isn't a mathematician Mar 23 '16 at 12:23

Seems reasonable to me. You could make a separate chat room for a specific topic, if you like.

I should point out, the same people who rant and rave about some contentious topic on a main site, possibly a meta page, may lose interest quickly on a side page like a chat room. There is no getting around this. People often play to the crowd, if there is no mob they turn to other pursuits. If you wish to experiment, just try to get someone who disagrees with you to write to you and discuss some matter through email, back and forth.

  • $\begingroup$ I know the downvote system usually implies someone debates this point, to which point do you debate and why? $\endgroup$ – frogeyedpeas Mar 25 '16 at 7:19
  • $\begingroup$ @frogeyedpeas, I'm not sure what you mean about downvotes. i did not downvote anything. If someone downvoted my answer or left a different comment, I do not see anything. Let's see, on MO and here, I have had some angry exchanges. I would ask these people to email me so that we could have a real discussion in private. That never came to anything, and some people refused to email me in the first place. $\endgroup$ – Will Jagy Mar 25 '16 at 18:00
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    $\begingroup$ @WillJagy I think frogeyedpeas is talking about the downvote on your answer. (Simply click on the score to see that your answer is currently at +3/-1.) $\endgroup$ – Martin Sleziak Mar 26 '16 at 9:46
  • $\begingroup$ @MartinSleziak thank you, that worked $\endgroup$ – Will Jagy Mar 26 '16 at 17:16

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