I am right next he machine in the same position. The AirPods connect. I am working form the same seat.
I have an updated card with an extension to the antenna in the case.
Wanted to report back to you that I am not seeing any dropouts, static or other audio abnormalities on my AirPods connected to my cMP running 10.14.4. I've been listening to music via iTunes for the last 20 minutes and it's been perfect.
I too installed an updated Airport card (BCM943602CD 802.11ac BTLE 4.2) a couple years ago. I don't routinely use my AirPods with this machine, so I can't say if maybe there could have been audio artifacts on previous versions of macOS (Mojave or otherwise). But I haven't seen any complaints about it here or elsewhere either, which makes me think that the problem you're seeing has something to do with your setup. Could be software, hardware or (IMHO most likely) a problem with signal strength or SNR. Perhaps one difference in our setups is that I used one of my cMP's WiFi antennas for BT (based on a helpful tip I think I read here way back when). The built-in BT antenna is located on the back panel of the cMP, near the PCI cards--pretty terrible location.
So you might want to experiment a bit. First try re-orienting your cMP so that the back of the machine is facing you to see if you notice any difference in the audio. If it drastically improves then you're going to want to address the antenna situation.
I should add one more variable highly likely to have an effect--do you have a USB 3.0 card and/or any USB 3.x peripherals operating nearby your cMP? If so, then step one is to unplug them. Personally I have experienced a lot of 2.4GHz interference from various USB 3.0 stuff (not just on my cMP but on other Macs too). It can *really* mess with Bluetooth, so check that out too.
Good luck.