The only issue is fuel economy, though you're not using refrigerant per se. I normally set it to manual mode (turn auto off) with the top down and direct the flow onto my feet and body. If you leave it in auto mode, the car will be trying to cool the planet
If BMW did not want you to use the a/c with the roof down they would have programmed it out, you actually have to go into the a/c menu to turn it off. The a/c is a 99.99% closed loop system on the refrigerant side as the loop isn't entirely sealed, there is a little leakage through the relief valve (<3x10^-6 mbar.l/sec) and hence they need refilling over time.
If BMW did not want you to use the a/c with the roof down they would have programmed it out, you actually have to go into the a/c menu to turn it off. The a/c is a 99.99% closed loop system on the refrigerant side as the loop isn't entirely sealed, there is a little leakage through the relief valve (<3x10^-6 mbar.l/sec) and hence they need refilling over time.