No one really knows what will happen in the new contract. Current thinking is that a significant military aircrew presence will remain. Civilian SAR tends to be crewed by the more experienced pilots. Funnily enough, the RAF crews, in some circumstances, are less experienced than their civilian counterparts (although there are also lots of RAF crews with huge amounts of experience). However, the younger ones make up for this to a certain extent with a large amount of training.
If (and it's a big if) the entire system was to go civilian there would be two effects. There would probably be a not insignificant number of military SAR aircrew looking for jobs in the new system. However, there will also be a lot more civilian SAR jobs. What the overall effect would be I cannot tell.
The comment from the RAF pilot (if anywhere near accurate) is not very well made but the sentiment is there. Obviously, everyone has to start somewhere, however there is a big difference between an ATPL pilot flying an R22 or Squirrel, and flying a S61 or S92 sized helicopter in atrocious weather. It goes without saying that the crews have to be experienced. This is not a problem that only affects civilian crews. From my understanding most of Bristow's pilots are either ex-military or have a lot of experience flying S61's in rig type work. I know a lot of the Bond Jigsaw pilots are ex-military.
The fact is that there are civilian SAR pilots out there with no military experience. If that is what you want to do, I wouldn't be put off by the scaremongering in the papers.