how do I delete multiple cells - shift cells left?

When I select multiple cells to delete, the options to “shift cells up” and “shift cells left” are grayed out.

Is there a way to access these options?

Yes. Use them without multi-selecting non-contiguous areas.

That is obvious but doesn’t help. I need to be able to select non-consecutive cells and delete, and shift-left, on a regular basis. This works great in MS Excel but apparently it doesn’t work in other applications.

I have the same issue, I solve it by "File>properties select ‘security’ tab, uncheck “Record Change”.
Hope this will help!

And what specifically that “same issue” is that is solved by turning recording of changes off? I ask because OP’s problem - i.e., simultaneous removal of multiselection with shift - is unaffected by the setting (which is also available in EditTrack ChangesRecord).