Google-sheets – Conditionally format if date is same/greater or smaller than current date

This is not possible as far as I can tell. Google's conditional formatting is not very robust.

Here is Google's Conditional formatting help, although I don't think it's very helpful in your situation. It doesn't appear you can even use a cell value for the conditional formatting.

EDIT:

I found this link recently. It's much more complicated, but you can do what you want using their Javascript API.

Here is what you can do:

1. RightClick B2 → select Conditional formatting → select Custom Formula is (from the List)
2. Enter the following formula in the textbox: =b2>=c2
3. Check the Background Color and select green color
4. Click on Add another rule
5. Select Custom Formula is (from the List)
6. Enter the following formula in the textbox: =b2<c2
7. Check the Background Color and select red color
8. Click on Save Rules
9. Highlight B2 and click on Paint Format option on the tool bar.
10. Now click on cell B3 and drag until cell - B117 (this should apply the conditional formatting on cell ranging from B3-B117)

And for your second condition (i.e., to highlight D with green if it is greater than or equal to E, red if it is less than E) - simply repeat the above steps by interchanging D2 for B2 and E2 for C2.