(Of course, in practice regular people by and large don't vote their shares.)
For the former, if at all possible, you should sell those, and invest in the general market: your job already gives you plenty of excess exposure to the fortunes of your employer, and your career gives you excess exposure to the general industry you are in. No need to concentrate your effective investments even more. Diversify.
For the latter: don't bother picking stocks as an individual investor. Just go with a low cost index fund (and they can vote the shares for you).
I'm not sure why I would care about what the board/management of some /other/ public company (that I don't work for) thinks about my vote. Almost certainly they won't think about it at all.
(There's an impeachment process. But that's not available for regular voters.)