Mozilla/5.0 (X11; Linux x86_64; rv:68.0) Gecko/20100101 Firefox/68.0 ID:20190320112939

I can't seem to be able to access the new avatar button with the tab bar, which is not great given that making the toolbar buttons accessible via tab and shift+tab is a feature that landed in 67 (bug 1436086).

This should have been fixed by bug 1536514 and it seems to be for me. Can you please provide exact STR? Are you tabbing to the group of buttons containing the Accounts button and then using right arrow to move to the Accounts button?

Note that there's also bug 1537647 (not yet fixed), but you should still see the panel get displayed when you press space/enter on the button.

I am attaching a small screencast showing the bug.

STR are basically ctrl+L to get into the location bar and then using tab/shift+tab to navigate the toolbar buttons.

I'm blind, so can't see the screencast. That said, tab/shift+tab alone aren't enough to navigate the toolbar buttons. In order to avoid cluttering the tab order (and thus to ensure an efficient experience), tab moves between "groups" of buttons. Once you reach the desired group, you use the right arrow to move to the button you want. For example, if the page actions aren't visible (no page loaded), with default configuration, you would press control+l, tab once to the Library button, then right arrow several times to get to the Firefox Accounts button.

Thanks for the detailed explanations, navigating works indeed with the arrow key once you reach the previous icon in the group, so my bug is invalid, good news :)