BGP VPNv4 VRF routes not sent to CE router

Did you verify that local and remote CE devices are in routing table?

show ip route vrf CUST-1 [prefix]
show ip cef vrf CUST-1  [ip-prefix]

I don't see ldp configured on PE device, so I don't know how you advertise labels in the mpls network.

Check route distinguisher, import and export route targets do they match on both sides:

vrf definition CUST-1
 rd 100:1
 route-target export 1:100
 route-target import 1:100

You can check your configuration against - Multiprotocol BGP MPLS VPN page 12

For way much more technology details and how to verify each step I would suggest excellent videos - MPLS L3VPN Part 2 with Narbik Kocharians

Both VRF definitions match.

The remote PE/CE and local CE routes are on the PE's. The remote CE is not advertised to the attached CEs in the same VRF.

Gateway of last resort is not set

      10.0.0.0/8 is variably subnetted, 3 subnets, 2 masks
B        10.10.10.0/30 [200/0] via 1.1.1.1, 07:39:12
C        10.10.20.0/30 is directly connected, Ethernet0/0
L        10.10.20.1/32 is directly connected, Ethernet0/0
B     192.168.100.0/24 [200/0] via 1.1.1.1, 07:39:12
B     192.168.200.0/24 [20/0] via 10.10.20.2, 07:39:12

PE2#show ip cef vrf CUST-1
Prefix               Next Hop             Interface
0.0.0.0/0            no route
0.0.0.0/8            drop
0.0.0.0/32           receive
10.10.10.0/30        172.16.2.2           Ethernet0/1
10.10.20.0/30        attached             Ethernet0/0
10.10.20.0/32        receive              Ethernet0/0
10.10.20.1/32        receive              Ethernet0/0
10.10.20.2/32        attached             Ethernet0/0
10.10.20.3/32        receive              Ethernet0/0
127.0.0.0/8          drop
192.168.100.0/24     172.16.2.2           Ethernet0/1
192.168.200.0/24     10.10.20.2           Ethernet0/0
224.0.0.0/4          drop
224.0.0.0/24         receive
240.0.0.0/4          drop
255.255.255.255/32   receive

PE2#show mpls ldp bindings
  lib entry: 1.1.1.1/32, rev 11
      local binding:  label: 19
      remote binding: lsr: 2.2.2.2:0, label: 19
  lib entry: 2.2.2.2/32, rev 7
      local binding:  label: 17
      remote binding: lsr: 2.2.2.2:0, label: imp-null
  lib entry: 3.3.3.3/32, rev 5
      local binding:  label: imp-null
      remote binding: lsr: 2.2.2.2:0, label: 18
  lib entry: 172.16.1.0/30, rev 9
      local binding:  label: 18
      remote binding: lsr: 2.2.2.2:0, label: imp-null
  lib entry: 172.16.2.0/30, rev 3
      local binding:  label: imp-null
      remote binding: lsr: 2.2.2.2:0, label: imp-null
PE2#trace
PE2#traceroute 1.1.1.1 so
PE2#traceroute 1.1.1.1 source 3.3.3.3
Type escape sequence to abort.
Tracing the route to 1.1.1.1
VRF info: (vrf in name/id, vrf out name/id)
  1 172.16.2.2 [MPLS: Label 19 Exp 0] 4 msec 5 msec 4 msec
  2 172.16.1.1 3 msec 5 msec 1 msec

PE1#show ip bgp vpnv4 vrf CUST-1
BGP table version is 21, local router ID is 1.1.1.1
Status codes: s suppressed, d damped, h history, * valid, > best, i - internal,
              r RIB-failure, S Stale, m multipath, b backup-path, f RT-Filter,
              x best-external, a additional-path, c RIB-compressed,
Origin codes: i - IGP, e - EGP, ? - incomplete
RPKI validation codes: V valid, I invalid, N Not found

     Network          Next Hop            Metric LocPrf Weight Path
Route Distinguisher: 100:1 (default for vrf CUST-1)
 r>  10.10.10.0/30    10.10.10.2               0             0 200 ?
 *>i 10.10.20.0/30    3.3.3.3                  0    100      0 200 ?
 *>  192.168.100.0    10.10.10.2               0             0 200 ?
 *>i 192.168.200.0    3.3.3.3                  0    100      0 200 ?
PE1#

PE2#show ip bgp vpnv4 vrf CUST-1
BGP table version is 7, local router ID is 3.3.3.3
Status codes: s suppressed, d damped, h history, * valid, > best, i - internal,
              r RIB-failure, S Stale, m multipath, b backup-path, f RT-Filter,
              x best-external, a additional-path, c RIB-compressed,
Origin codes: i - IGP, e - EGP, ? - incomplete
RPKI validation codes: V valid, I invalid, N Not found

     Network          Next Hop            Metric LocPrf Weight Path
Route Distinguisher: 100:1 (default for vrf CUST-1)
 *>i 10.10.10.0/30    1.1.1.1                  0    100      0 200 ?
 r>  10.10.20.0/30    10.10.20.2               0             0 200 ?
 *>i 192.168.100.0    1.1.1.1                  0    100      0 200 ?
 *>  192.168.200.0    10.10.20.2               0             0 200 ?

AS path on both sides is the same (the same AS number on both CE routers, loop preventing mechanism most likely is blocking route import).
Try to issue on CE routers:

(config-router)# neighbor 1.1.1.1 allowas-in
clear ip bgp *

(config-router)# neighbor 3.3.3.3 allowas-in
clear ip bgp *

Other solution could be to configure as-override on PE routers.
(config-router)#address-family ipv4 unicast vrf CUST-1
(config-router-af)#neighbor 1.1.1.1 as-override

There is a rib failure for:
r>  10.10.20.0/30    10.10.20.2               0             0 200 ?

r>  10.10.10.0/30    10.10.10.2               0             0 200 ?

As this is a VIRL environment i think I am looking at a bug in the environment.
(%AMDP2_FE-6-EXCESSCOLL) on all devices (IOS 15.5 code).

And about the RIB failures, those are due to BGP announcing routes that are known with a better AD (and discarded).

Just to confirm. You have double-checked the vrf assignment of the interfaces on your PE's attached to your CE's. Also when you do a traceroute on the VRF from the far end CE, it is making it to the PE router attached to the CE with the issue?

PC-1> trace 192.168.200.10
trace to 192.168.200.10, 8 hops max, press Ctrl+C to stop
 1   192.168.100.1   1.252 ms  0.252 ms  0.165 ms
 2   10.10.10.1   1.293 ms  0.297 ms  0.320 ms
 3   172.16.1.2   1.469 ms  0.607 ms  0.526 ms
 4   10.10.20.1   1.189 ms  0.473 ms  0.557 ms
 5   10.10.20.2   1.894 ms  0.955 ms  0.581 ms
 6   *192.168.200.10   2.357 ms (ICMP type:3, code:3, Destination port unreachable)

PC-1>


This is an issue... it's going through the IGP and I am seeing the IGP... this should not be the case when MPLS/BGP is fully working...

Hop1 = PE1 (CE router)
Hop2 = PE1 (PE1 Cust-1 VRF)
Hop3 = P1 (Core P router IGP address)
Hop4 = PE2 (Cust-1 VRF)
Hop5 = CE router
Hop6 = Should be PC-2

Are you wanting to not see the MPLS hops and just want to see a CE to CE hop?  If so, you need to disable the TTL propagation in MPLS.

Keeping the TTL is good for troubleshooting though. In productions environments it's usually disabled.