Hi an welcome to network engineering!
Customer1's 126.96.36.199 cannot communicate with Customer2's 10.1.2.2, and Customer1's R2 is not supposed to know about Customer2's 10.1.2.x subnet.
It appears that both customers use the same addressing for their end subnets (10.1.[1-4].x). That would imply that they are not using the same L3-VPN (sometimes just called "VRF"), else that would be a pretty bad job of network adressing.
However, different customers being in separated VRFs is the actual purpose of L3-VPNs: to keep customers separated. So anyhow, in any case, R2 is not supposed to know a path to Customer2's 10.1.2.2 (which is somewhere beyond CE2 and R4).
Only if somewhere "upstream" in the network (i.e. one one of the PEs), either..
- routing information were leaked from one customer's VRF into the other's
- or a link connecting the two VRFs were set up on a PE or a multi-VRF CE, with suitable routing information being disseminated into both customer's VRFs, as in
redistribute static or
- (added later) or - at a suitable place in the MPLS infrastructure - a device (most probably a firewall) is added, which has "legs" into more than one L3-VPN/VRF, and suitable routing information.. (see above). This device will then act as the well-defined gateway between Customer1 and Customer2 (and may perform the required NAT sorcery if addresses of C1 and C2 overlap)
... communication from one VRF to the other might become possible. But then, Customer1 and Customer2 would still not be able to communicate because of the address overlap, unless they were to resort to some dreadful NAT magic.
However, since Customer1's 10.1.2.x subnet is directly attached to Customer1's R2, R2 will always forward traffic towards 10.1.2.x through that interface, whatever routing information from whatever routing protocol is being disseminated into Customer1's VRF/MPLS-VPN and further down into Customer1's own routing domain, where it might be picked up by R2 by some IGP routing protocol such as OSPF, EIGRP or RIPv2. In terms of route preference, nothing - not even a static route - is better than a connected route/a directly attached subnet (yes, we'll keep the can of worms called "PBR" closed for today).