While Robert would have been called up, because of his former experiences in the army (the Boer War), we don’t know if Strallan was in the army before. Robert did not fight in Belgium, France, or any other fronts, but he did have a job to fulfill ‘back home’.
Besides, he might have simply enlisted and be found good enough to join, especially by the end of the war, the pickings were getting rather slim.
Carlisle not fighting might be because of a pre-existing condition or maybe he simply bought his way out. Plus he wasn’t all that young either - in my eyes he suited Lady Rosamund more than Mary (imagine, Roz and Richard - they could have conquered the world).
This is all pure speculation, during my lunch hour, without having done any research at all, so I may be completely off base.