They are locally significant but if R1 established its neighbor interface with R2 via 10.0.0.1, it will only advertise routes to R2 learned via OSPF Routing Instance 1.
In order for R2 to learn routes learned via OSPF Routing Instance 2 from R1, they need to be redistributed into OSPF Routing Instance 1.
When you see references about being locally significance is that you can flip the routing instances, for instance
router ospf 2
network 10.0.0.1 0.0.0.0 area 0
router ospf 1
network 10.0.1.1 0.0.0.0 area 0
and let's say R2 has:
router ospf 1
network 10.0.0.2 0.0.0.0 area 0
As you see, the OSPF process ID does not match but they can become neighbors.
HTH,
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Edison.