Financial independence (FI) is not binary: achieving FI is a journey, and I believe that having an emergency fund is one step in that journey.
For those of us who want to invest every dollar, it might be tempting to try and go without an emergency fund. While I get that it is tempting to game this aspect of your personal finances, trust me, you still need one. This is the bedrock of your portfolio.
Remember: The whole reason we strive for financial independence is so we can buy our freedom from the problems and stress that money can bring into our lives.