Don's observations make interesting reading; but in this case, I think the problem may lie in the Scotland's People Transcription.
I am going to investigate in more detail, later today; and will post my findings.
Also depending on what they are, I will report them to Scotland's People, as I suspect that the problem originates there, as the Primary Source.
FMP (and possibly Ancestry) probably access SP by active live links; or by downloads, otherwise why the same problem?
I have considerable experience of writing programs; and trouble-shooting of programs from many sources, so devising methods comes readily to me. (Can Mhor!)
How did I find it?
I first duplicated your Searches for Robert Bruce, in Find My Past, with results from the 1861 and 1881 Censuses only, just as you had encountered.
I then searched for the son James, as he appeared in both; and being only 3 in 1861, there was a fair chance that he would have been at the family home in 1871, at 13 years old.
If he had not shown up readily in the 1871 Census, I would have tried others from the 1861 and 1881 results, with the proviso that they were likely to be alive for the 1871 Census and in that family household.
"Thir's nae jiggery pokery in'it!"
I have effectively finished my personal Family History in Scotland (25 years), leaving one major quandary regarding the origins of one line in England-