Short Answer: Yes!
Long Answer: Yes, Open Mesh Access Points (AP) are safe and secure because it runs its own Wi-Fi network, separate from any other networks you already have running. You'll also want to ensure you have the 'Gateway LAN Block' setting enabled to isolate your wireless clients from having access to anything wired into your OM AP. That means any POS (Point of Sale) or other systems you have do not share access.
To ensure the OM APs remain on a separate network from any other networks you want to keep secure, be sure not to bridge your secure networks through the OM AP. For OM2Ps, plug the Internet connection into the OM AP through the port labelled '18-24v POE'. Avoid bridging any networks with private information into the port labelled '802.3af POE' on the OM AP.
For example, it's safe and secure if you follow this setup:
Modem/Router ---> POS System --(18-24v POE)--> OM AP.
Do not follow this setup:
Modem/Router --(18-24v POE)--> OM AP --(802.3af POE)--> POS System.