if you can use column C as a helper column to have a date in every row, the conditional formatting would be pretty simple:

you’d just have to set C1=A1, then you can use the formula at the top for the other rows and base the conditional formatting on column C.

edit to add: I wasn’t sure how you were picking which date to highlight, so I just set it up to enter a date in D1 and highlight any with that date.