The command you need is
electric-indent-local-mode. You can use this to turn off electric-indent-mode in any buffer by calling it manually:
M-x electric-indent-local-mode. This is a toggle, so calling it again in the same buffer turns it back on again.
To do this automatically from your init file, you need to set up a hook. First, define the hook:
(defun remove-electric-indent-mode ()
Then add it to the appropriate mode hooks. To turn off electric-indent-mode for the LaTeX mode provided by AUCTex, use this:
(add-hook 'LaTeX-mode-hook 'remove-electric-indent-mode)
For the default texmode, use:
(add-hook 'tex-mode-hook 'remove-electric-indent-mode)
The same pattern holds for any other mode you want to turn off electric indentation.
For more details on mode hooks, see the built-in Emacs manual node
[(emacs) Hooks]. You can get there from Emacs via
C-h i r m Hooks <enter>:
C-h for help,
i for info,
r for read the manual,
m for menu item, and
Hooks to pick the menu item. (or you can follow the link above to see the html version).