This answer was originally written when add-ons were the only alternative. Now that Firefox can natively select multiple tabs, that is explained first, and the add-ons later.
Firefox can now natively select multiple tabs from the tab bar.
Native tabs selection
To select multiple tabs, press Ctrl or Shift and followed by a click on the mouse primary button for discontinuous or continuous selection respectively. The selected tabs can be managed from the tab context menu, keyboard shortcuts and drag and drop.
This feature is available from the recent releases of Firefox Quantum, and has been mentioned in the Firefox 64 release note.
Enhanced tab management: You can now select multiple tabs from the tab bar and close, move, bookmark, or pin them quickly and easily
The hidden configuration named
browser.tabs.multiselect has been included at least from Firefox 62 however, with limited implementation. Some differences can be observed:
- Firefox 62 can select multiple tabs (disabled by default), but limited to bookmark, reload, close selected tabs.
- Firefox 63 can select multiple tabs (disabled by default), but limited, yet can additionally move to new window, and close other selected tabs by drag and drop.
- Firefox 64 can select multiple tabs and do everything as per release note.
Tested using Firefox 62, 63, 64 on Linux.
Tabs selection with add-ons
Before tabs selection became native, there are already some add-ons that can do similarly. Firefox with add-ons however, does not behave exactly same as native Firefox or Chrome does. The main reason: Firefox Quantum add-ons are limited by the design of the modernized Firefox add-ons.
Anyway, I have noted two add-ons that can select multiple tabs:
Multiple Tab Handler by Piro (piro_or)
Allows users to select multiple tabs in a window and perform operations on them.
MultiSelect Tabs by mike_conley
Provides feature to close multiple tabs.
Both add-ons can be installed in Firefox Quantum. Multiple Tab Handler uses a button in the main toolbar, and on the other hand, MultiSelect Tabs uses the sidebar to provide the functions.
Tested add-ons using Firefox 57, 59 on Linux.
TL;DR Firefox can now natively select multiple tabs. Firefox 62 and 63 can do already, but limited and disabled by default. User can now forget the add-ons and do natively.