... But you haven't answered in the question kindly asked by @roytam1: Have you tried a fresh New Moon 28.8.0a1 profile (with no extensions) and try gmail behaviour there?
In your screenshot (where NM28 is run under Win7) I see you have installed uBlock Origin (legacy), Disconnect and NoScript; they are bound to conflict with each other - also bear in mind that NoScript is explicitly incompatible with Pale/New Moon and UXP based browsers, so it's better to be avoided! IMHO, your gmail issues arise from using too many/incompatible content/script blockers.
Second, you were told earlier (I think in the original thread) that you are not to compare latest versions of browsers (latest Chrome and Chromium based forks, latest Firefox Quantum/Browser) with the older-Firefox based forks in terms of behaviour on heavily-scripted sites; Google and the rest of the gang (e.g Facebook) always target the latest browser versions on new era hardware and OSes (and it can be argued that browser vendors have to always catch up with Google and gang in order to retain compatibility with whatever alpha Javascript/CSS features they are implementing on their sites) ...
You only have yourself to blame for this "great" problem of yours... New Moon is mainly targeted for XP (and for the few of us on Vista), where official PM won't run; thus, XP+Vista users of NM won't ever be faced with the problem you've created...
As for NM+PM on Win7 and higher, what you report is to be expected - don't use both browsers, as, of course, they'll share the same profile location - but, and this is worse, New Moon isn't anymore just PM for XP; the codepaths have diverged (and this is even more pronounced in the case of Serpent52/Basilisk52); e.g., the NSS library used currently by MCP in official PM is different to the one used in NM, so expect profile corruption to occur when the same profile folder is being alternatively shared by the two browsers.
If you still insist on using both NM28 and PM28 on the same computer (and windows account), then you should be using the official Pale Moon Portable package,
http://www.palemoon.org/download.shtml#Portable_versions
so that New Moon maintains a discrete profile and PM28-portable another discrete one...
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To cure your self-inflicted issues:
1. Uninstall official PM28
2. Back-up the corrupted NM28 profile, in order to salvage what can be salvaged from there...
3. Delete the original, old (saved elsewhere), NM28 profile.
4. Make sure you have the latest NM28 version, launch it and you should be in a new fresh profile - then start anew with configuring it the way you like - but heed to step 5...
5. Avoid installing too many blockers - ublock0-legacy alone would suffice.
6. When you're finished configuring NM28, exit it.
7. "Install" the portable version of official PM28 - that version should always be launched via the palemoon-portable.exe launcher (you can create a desktop shortcut for it) and with NM28 exited.