It is still true, most common refrigerants still have quite high GWP [1]. Not as bad as in the 70's, but the transition to neutral gasses is not ready yet. And then there is also all the old installed systems still running.
It's a very unfortunate outcome of phasing out CFCs that they have in many instances been replaced by powerful greenhouse gases. HFCs are slowly phased out as well, but there are still a lot of harmful gases out there.
The typically used R32 does not cause any ozone issues. It is a climate gas, but only if it escapes from the pipes which it doesn‘t if properly installed.