Does anyone know if any Chinese pcb makers are taking orders at present?

JLCPCB.com was already up and delivering several weeks ago.
Just stay away from the economical shipment option, this might take ages to show up at your place.
The DHL express shipment took 4 days to arrive at my place several weeks ago when they were still in lockdown.
 
I recently discovered aisler.net as european alternative.
If 3 boards are sufficient, it's faster and roughly the same price as chinese (boards cost a little more, shipping is cheaper, no taxes to pay as it's shipped from Germany).
They are pooling PCB's and work with different european board-houses.
PCB quality is top-notch.
If you need lots of PCBs, then China is cheaper.