Can a first author omit the "equal contribution" for a publication on the CV?
Let's be clear: You are trying to claim more credit than you are due by omitting information. Phrased like this, does this sound ethical to you? If it does, you may want to re-consider your standards. If not, you got your answer.

As a general rule in life, of course, you want to be treated the way you treat others. That means being generous in your praise, and modest in your claims. In the current context, you can't reasonably be expected to only put the "equal contribution" asterisk only next to the other author, but you'd probably be annoyed if your coauthor reversed the order of first and second author in their CV. So don't do the equivalent on yours.