@matseac 

It would be my guess that the issue is not with the Access Point, but rather the inter vlan traffic itself.

Check that the 2x vlans can communicate with each other on the switch / router.    The AP wont forward between vlans, it will simply dump the data from the WiFi to the default gateway / VLAN you tell it, that is where the communication between the vlans happens.

@Philbert First, thanks for your answer.

I may have been unclear or left out some information here, so I'll add some more detail:

Both VLANs can actually communicate via the router. I can ping the AP at 10.0.0.2 and all other wire-connected machines (somewhere in 10.0.0.1 to 10.0.0.254) from my AP-connected machine (10.0.1.176). The only machines I cannot ping are the ones connected with the same SSID and, consequently, using the same VLAN. My understanding is that Client Isolation would be what prevents this, but it's turned off (and cannot be turned on anyway). 

@matseac 

Hey

Would you be able to tell us what Router you have?  How did you create the VLANs on the router?

Just thinking out loud here and perhaps I am missing something, but VLANs require a switch to handle the traffic, these cant be established by a router.. not aware of any routers that have VLAN capable switch built in.

Did you have this working before or just setting up?   What are you trying to achieve?