For Tab Session RestoreManager, check whether there is a setting to control whether it opens tabs in the background. I'm pretty sure an extension has the ability to determine whether a tab it opens is made active or not.

For externally launched documents, perhaps changing another of the "InBackground" settings would help. Could you check:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful or accepting the risk.

(2) In the search box above the list, type or paste inback and pause while the list is filtered

(3) Double-click the following preferences to switch the value from false to true as desired:

• browser.tabs.loadInBackground - when you right-click > Open Link in New Tab, or Ctrl+click, or middle-click a link (default = true; this is the one on the Options page)

• browser.tabs.loadDivertedInBackground - when a link was coded to launch in a new window and Firefox switched it to a new tab instead (default = false; try changing to true)

• browser.tabs.loadBookmarksInBackground - when you direct a bookmark to a new tab (e.g., using right-click > Open in New Tab, or Ctrl+click, or middle-click a bookmark) (default = false; doesn't seem relevant to external links)

Can you get it working the way you like?

Start Firefox in Safe Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration is causing the problem.

• switch to the DEFAULT theme: "3-bar" menu button or Tools -> Add-ons -> Themes
• do NOT click the "Refresh Firefox" button on the Safe Mode start window

• https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-using-safe-mode
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems