The term Barelwi is needless, in my opinion. We already have clear and meaningful identifiers: Sunni - Ashʿarī/Maturīdi. Imams who preach this label and go around promoting it would be better served teaching the actual creed that Imam Ahmad Rida Khan followed, and making it clear that he was firmly and unquestionably Sunni. There is far more value in that than in defending or shouting a label that adds no theological clarity and only confuses people.
I would argue that the label "barelwi" is a necessity. Because wolves started wearing sheep's clothings, sheep needed to dye their wool or get "wool-mark"ed differently. Otherwise, the risk of getting their lamb eaten/stolen becomes very high. This is a time-honoured tradition of addressing any new fitna that arises.
For laypeople, the term only creates confusion. Labels create groups, and extra group labels inevitably create fault lines, even when no new beliefs are being introduced. Whatever the intention, that’s the practical outcome on the ground.
Who are these laypeople you are worried about? Are these arabs or sunnis outside sub-continent? If so, then we "barelwis" always go about with sunni label; but if that layman confuses deobandis to be sunni too, we bring out the barelwi card. As you see, "barelwi" label is not to cause confusion, but to remove it and to disambiguate. We are not people of
taqiyya, so we don't hesitate to take the card/badge when needed.
If by laypeople you mean those less well-versed, simpletons, then I would say that such layman wouldn't even know what being maturidi means.
As
@abu Hasan mentioned this label was accorded to us by dayabina. Other labels are quburis, raza khanis etc., but "barelwi" is the one we are happy and very proud to wear. If it grates laypeople (who you're very concerned about), so be it!
Barelwi is a sociological tag, not a creedal school.
On one hand, you profess ignorance about the differences; on the other, you have convinced yourself that the tag is sociological! How have you arrived at such conclusion, despite ignorance?
No, the tag is creedal, since the differences with deobandis is creedal.