Lizzie
You have effectively asked four separate questions, which I will try to answer succinctly.
1) The Peace Pledge Union (PPU), founded 1934, is the main British secular (i.e. neutral on the question of religion) pacifist organisation. As such it opposes all war, and was active in the cause of peace throughout WW2, including, especially, campaigning against mass bombing of German civilians and campaigning for the relief of starving children in occupied countries, particularly Belgium and Greece - Oxfam traces its roots from this effort. The PPU also, obviously, supported conscientious objectors (COs) to military service, for whom the law quite properly provided, whatever your father and your mother's brothers may have thought about it.
2) Contemporary official records of conscientious objectors were retained so long as conscription itself lasted, but after the final discharge of the last conscript in 1963 the authorities decided on a clear-out, and all records of individual CO cases were destroyed except for those heard by the Midlands Tribunal, which were retained as a sample of how the system worked, and are now in the National Archives. Partly because of the gap which the clear-out left for family history and other researchers, the PPU has begun the mammoth task of creating a database of every British CO of whom a trace can be found - 7000 names so far, of whom about half are WW2. The database includes notation of where records, if any, relating to a particular CO still exist (and they do in various places), so the PPU is a useful and logical first stop in enquiries about any CO, and if he/she is not already recorded, a record is automatically begun.
3) Regarding your mother's younger brother, you now seem to have some doubt as to whether he was actually a CO. Without fuller detail, it is difficult to be precise, but I can say that if he was around 20 when he went up to Oxford, then presumably he began his degree course around 1937. There is virtually no question that he would have been permitted to finish the course - ?1940, although some courses were actually foreshortened, resulting in what were known as 'war degrees'. It seems unlikely that he would have been able to spin out any studies for the entire duration of the war, and, as I have indicated, universities themselves manipulated things to actively discourage this. This does, therefore, raise the possibility that he was, indeed, a CO. If that were the case, then two further possibilities arise: either he was permitted to go straight to a Baptist theological college to train for the ministry - probably a two-year course, after which he would have been ordained; or he was required to do some alternative service, such as farming, forestry or menial work in a hospital, until c 1946, after which he would have gone to theological college, and then been ordained. Have you checked Oxford University records, his Oxford College records, records of the Baptist Union regarding their ministers?
4) Regarding your mother's eldest brother, if he was around 30 in 1939, he would certainly have been of military age throughout WW2. I am extremely doubtful whether butchery would have been a reserved occupation, thereby inhibiting call-up, and if he appeared to be medically fit with no disability then a question remains. However, men were sometimes rejected on medical grounds that by no means inhibited civilian occupations; there were strict rules about eyesight, for example, and there could be apparently minor foot or leg problems which were seen as potentially causing difficulties for marching or other kinds of military activity. There is a further possiblity that his entire war service was spent in Britain - this did happen - so it was not seen as interesting. I can only speculate.
I hope this helps.
Fitzjohn