IRULE to remove a header value

Use replace instead of insert, which will just add another header. Try putting in the following log statements before after the header replace to see what headers are coming in and what are being sent out.

when HTTP_REQUEST { 

  foreach x [HTTP::header names] {
    if { $x equals "X-MS-Forwarded-Client-IP" } {
      log local0. "Incoming $x: [HTTP::header $x]"
    }
  }

 HTTP::header replace X-MS-Forwarded-Client-IP [IP::remote_addr]

  foreach x [HTTP::header names] {
    if { $x equals "X-MS-Forwarded-Client-IP" } {
      log local0. "Outgoing $x: [HTTP::header $x]"
    }
  }
}

you should see something like this in the logs, e.g. a request from 10.12.12.1 client-ip but with a X-MS.. header of 11.11.11.11, the F5 is replacing the header with 10.12.12.1 as per rule ...

curl -vv -H "X-MS-Forwarded-Client-IP: 11.11.11.11"  http://10.10.10.10

Rule /Common/test1 : Incoming X-MS-Forwarded-Client-IP: 11.11.11.11
Rule /Common/test1 : Outgoing X-MS-Forwarded-Client-IP: 10.12.12.1