It's obvious why two routers in the same OSPF domain cannot have the same router ID. But requiring unique router IDs on OSPF processes running in different VRFs is probably too harsh, although it does prevent confusion if two VRFs ever get connected through a customer site. Anyhow, if you have overlapping IP addresses on loopback interfaces in different VRFs, OSPF process might not start.
Here's a short example: two VRFs have loopback interfaces with the same IP address. Perfectly legal setup from the MPLS/VPN perspective.
c7200#show ip vrf interfaces
Interface IP-Address VRF Protocol
Lo1003 10.0.0.1 EIGRP_OSPF up
Lo1001 10.0.0.1 OSPF_1 up
However, when you try to configure the second OSPF process, it fails to start as it cannot get a box-unique router ID. You have to enter a different router ID manually.
Enter configuration commands, one per line. End with CNTL/Z.
c7200(config)#router ospf 1 vrf OSPF_1
c7200(config-router)#network 0.0.0.0 255.255.255.255 area 0
c7200(config)#router ospf 3 vrf EIGRP_OSPF
%OSPF-4-NORTRID: OSPF process 3 cannot pick a router-id.
Please configure manually or bring up an interface with an ip address.