PureBrowser is very uncommon and it has a very uncommon user agent string. Uncommon user agent strings can be used to fingerprint a user, so it is a privacy concern.
I suggest changing it to something common, like the Tor project does:
Mozilla/5.0 (Windows NT 6.1; rv:60.0) Gecko/20100101 Firefox/60.0
Additionally, this fixes another problem where users cannot install extensions from https://addons.mozilla.org/ because Mozilla doesn’t recognize the browser as Firefox.
Firefox also comes with privacy.resistFingerprinting option in about:config, which automatically changes the user agent in addition to a bunch of other tweaks to resist fingerprinting.
This can possibly break some websites, so it may not be the best solution, but it is worth considering so I will mention it anyway.
Just note that Firefox only launches as a window, not maximized, when set to ‘true’. I found out the hard way.
Yes, that is intentional. It is possible to fingerprint the user via his screen resolution, which can be done when browser is maximized.
privacy.resistFingerprinting works around that by starting in a windowed mode.
That is for this reason it’s recommended to change the user agent string to a value similar to what you suggest on PureOS tracker wiki:
https://tracker.pureos.net/w/troubleshooting/firefox_compat_mode/
Setting the OS to Windows 7 instead of Linux as you do means preferring privacy a bit more than usability, for the occasional uses of it.
That said, the privacy concerns have already mentioned in PureOS tracker Task 247: https://tracker.pureos.net/T247
In the task description there is a link to Panopticlick https://panopticlick.eff.org/ which demonstrates how many other browser settings may be used for fingerprinting. I ran it and my particular setup could be fingerprinted much more because of the HTTP_ACCEPT headers (partially dependent of the preferred languages settings), the screen resolution and color depth and the system fonts set than of the user agent string.