It's 5:45 AM here and I need to get to bed. There should be others that can help, now that you have provided a bit more info.
If the cisco if really using vlan 1 for the native vlan, then a pc should get an ip address from the ip subnet associated with the base bridge interface.
If it doesn't then the cisco may be tagging vlan 1, and that won't work if the cap ax needs to communicate over the untagged vlan. I know nothing about capsman or wireless config on MikroTik, I have no MikroTik routers with wifi (only RB760iGS and RB5009), and use Ubiquiti Unifi APs at home.
So I don't know if the Capsman needs to communicate with untagged traffic or not.
If what @atomant said about the Cisco APs working and their wifi clients are getting ip addresses from the RB4011, then it seems there is a working connection between the RB4011 and the Cisco 2960 via the sfp. So there must be something that the cap ax is using that the cisco APs are not.
But we haven't seen the cap ax config, all we have been told is that the cap ax works when it is connected to one of the RB4011 bridge-ports (that all appear to be configured as trunks, with pvid 1).
So what the cause of the incompatibility is, I don't know.
While it is best practice to avoid using vlan 1, I don't think that using vlan 1 is what is causing the problem, unless the cisco is tagging vlan 1, and we were told it is not.
Having all ports configured as trunks is more of an issue in my opinion, (but we know nothing about how this switch is being used).
It's been a while since I have used Cisco switches, about 5 years, and then they were not using latest IOS version. So take anything I say about Cisco config with a grain of salt.