Certain breeds, such as Jacob, Shetland, Hebridean have indeed become so popular in recent years that they are no longer considered rare by the RBST. They are however traditional breeds with specific genetic traits which it is in our interests to conserve. This is not to say of course that the more 'commercial' breeds do not also have genetic traits that we want to conserve - of course they do, but their survival at the moment seems assured. The wider the genetic diversity of sheep in general the better - the more we will have to play with when we do need to use their genes in a changing world. It may well be that some of today's biggies in a few decades could themselves become the rarities, and then it will be their special characteristics that we need to conserve.
No I am not saying that the RBST is there to make sure that rare breeds remain rare - its track record shows that to be untrue. I am saying that rare breeds do not necessarily have to become popular in order to survive, if that survival requires them to change from their true type.
The answer to the question of surely if a Portland is born to two Portland parents, then it must be a Portland seems self evident - of course it is. I don't know enough about Portlands to know their history, but I believe that with some breeds there is a suggestion that 'foreign blood' has been introduced at some point and that this can be identified by eliminating certain traits. In Hebs it's white spots, wool on the legs, Roman noses, Scrapie resistance type ARR, too much size; in Jacobs it's pink noses, too much black and so on. So if a lamb doesn't quite fit the description/standard (there is a difference) then it is suspected of not being a 'purebred' lamb. Genetically, by culling all pink-nosed Jacobs, you cannot of course eliminate all the 'foreign blood' which has caused them to appear, but it seems to make people feel better. The phenotype ie what the animal looks like, may only loosely reflect the genotype ie it's genetic makeup, as not all genes are expressed. This is also how certain phenotypic expressions may suddenly appear in lambs from 'true to type' parents - also known as throwbacks.
My feeling is that in most breeds the mixing happened so far back that there is not much point in eliminating suspect animals now, but on the other hand the breed societies do have to draw the line somewhere. If it's a case of 'anything goes', then breeders will be adding a little bit of this and a little bit of that and as Robert has pointed out, the true genetic make-up of the breed will quickly become diluted.