As I mentioned on another recent post of yours, this depends on whether this is a list of three foods (in which case lots of variants, and even the word order would not matter) or if it is the name of the Scottish National dish.
I think most people will accept this as the dish, and they would no more accept turnips, swedes or rutabaga than they would accept banana and toffee pie instead of banoffi pie. So I would not accept turnip or turnips.
Notice that in the product description they use potatoes (plural) and swede (singular).
On this more technical question of singular versus plural, the first and most important thing is that there is no doubt in Gaelic. Buntàta does not have a plural and snèap's plural is dubious at best. In English, there is no doubt that these are countable when bought - you would buy potatoes/tatties and turnips/neeps/swedes (not sure about rutabaga though). But once they are mashed and no longer countable, I think both singular and plural are acceptable. One may be more common in any given dialect but it is not a big issue.
That is except for tatties. You cannot say tattie unless you are talking about a tattie. This is a very rare arrangement in Gaelic and English, but quite normal in Welsh - they even have a name for it. They would say that taten/tatysen (= tattie) was the singulative of tatws (=tatties).
I was offered three choices: snèap, snèip and snèapan. Of these, snèap is the currently preferred form. Snèip is a valid variant (according to Mark and Dwelly) and snèapan is what any reasonable person would expect the plural to be (so I am sure it gets used in practice). AFB gives snèipean as the plural, but I suspect this is just the plural of the variant snèip that is the older version according to Dwelly. Mark does not give a separate plural, saying the singular means 'turnip(s)'.
All in all, I think this question is teaching us nothing useful, as the differences are debatable and well beyond the level of Gaelic of this course.