Same issue as here, but the solution does not work: Can’t Shift Click in TBC Classic
Shift + Click (or right click) does not work for me. I cannot split stacks, link items in chat, or open up the socket screen on items. I have tried disabling all addons and resetting key binds to default. Nothing works…
This issue is only present on some of my characters.
1) Classic has its own Bug Report Forum.
2) What do you get back when you do /dump GetModifiedClick("SPLITSTACK")? If the split stack option is correctly bound to the shift key, the output of that line should include something like [0] = "SHIFT" (format from memory, but something about shift even if not exactly that line).
If it isn’t properly set, you can use the SetModifiedClick command to change it back.
/run SetModifiedClick("SPLITSTACK", "SHIFT")
The other options for item links, socketing, etc can be found in that link.
Oh, and make sure to save your keybinds afterward if you do run that set function.
We had the same problem and were able to fix it by editing this file in Notepad:
C:\Program Files (x86)\World of Warcraft_classic_\WTF\Account[youraccount]\bindings-cache.wtf
We deleted the lines that looked like this while the game was open:
modifiedclick NONE SELFCAST
modifiedclick NONE AUTOLOOTTOGGLE
modifiedclick NONE MAILAUTOLOOTTOGGLE
modifiedclick NONE STICKYCAMERA
modifiedclick NONE CHATLINK
modifiedclick NONE DRESSUP
modifiedclick NONE EXPANDITEM
modifiedclick NONE SPLITSTACK
modifiedclick NONE PICKUPACTION
modifiedclick NONE PICKUPITEM
modifiedclick NONE COMPAREITEMS
modifiedclick NONE OPENALLBAGS
modifiedclick NONE QUESTWATCHTOGGLE
modifiedclick NONE TOKENWATCHTOGGLE
modifiedclick NONE SHOWITEMFLYOUT
modifiedclick NONE SHOWMULTICASTFLYOUT
Then saved the file and did /reload in the game. The problem was gone. Then we logged out and logged back in and the problem was still gone.
tyvm kind sir
Ma’am, but you’re welcome. 
Thank you, ma’am