Ok, let's analysis each case:
1): include MBIST logic in the scan chain. If both MBIST and scan pass, then you think this chip works.
2): exclude MBIST in the scan chain. MBIST logic can't be tested by scan. But if there is some defect in the MBIST logic, do you think it can pass MBIST test?
So, I think exclude MBIST logic in SCAN chain is ok.
You could only not included the flop which will impact the clock or add the logic in the rtl code to ignore the mbist when the scan is enable for example.
I think whether or not you include the MBIST logic in the scan chain are all ok. Now you have problem with the scan chain if you want to include the MBIST. I think you can just ignore the MBIST. If you have time, I also prefer you debug out why this is some issue and how to fix it.
In our previous project, we exclude the MBIST logic in the scan chain.
Thanks