Is there a listing of the minimum browser versions required to use JIRA 7.1 or cloud available? All that I'm able to find is "Latest version on latest OS" for most platforms, as opposed to "Firefox XX and up," and that's probably for a very good support-y reason.
I'm interested specifically in:
Firefox Quantum 66.0.3 on Ubuntu Linux 14.x
Safari 9.1.3 on Mac OS X 10.9.5
Firefox 3.6.12 on Mac OS X 10.9.5
Anyone have a good idea whether these browsers should be "good enough" for JIRA, if not for official support?
No. Atlassian test with the latest versions of browsers when things are released, so you can usually rely on "my browser is quite recent so it should work", but they don't do broad-spread testing across huge ranges of browser versions. It's too much work, and it is far easier to just say "the latest stable versions of browsers today are x, so test against those X's and if older browser users have an issue, get them to upgrade".
Having said that, all three cases you list are things Atlassian are (roughly - don't think they bother with Ubuntu 14, as the current "good" version is 18 for example) testing against, but all of those browsers should certainly meet "good enough"
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