As we know the process id is locally significant then why do we need to redistribute the network in ospf between two different proceess id for end to end connectivity ?

Process-id is locally significant but try to understand when we run two different process on a single router then by default routes recieved in one process are never given to other lets take an example

Now considere this example in which r2 is running process 1 on interface connected to r1 0/0 and process 2 on interface connected to r3 0/1 so when routing information is received from r1 on interface 0/0 will be given to process 1 on r2 simillarly the routing information from r3 is recieved on interface 0/1 will be given to process2 on r2 so by default two different process do not exchange routing information so we have to redistribute

now considere another case on r3 ospf 2 is enabled on interface 0/0 and 0/1 so routing information recieved on both the interfaces will given to process 2 only so no redistribution needed redistribution between the different proceses is needed when on single router we run multiple process on different interfaces.

In OSPF database is built according to process ID.So for two different process ID's database will be seprate and SPF run will be for partciular process.

So if you want two processes to communicate you have to perform redistribution.