I'm usually pretty sniffy about family stories, although I have been known to admit that there is often an element of truth in them. I'm also on record as saying that I don't believe in coincidences.
Sir Isaac Newton was born at Woolsthorpe Lincs, which is where your Robert Thompson baptised children. Coincidence #1
Sir Isaac had a half brother Benjamin Smith who baptised a daughter Hannah in Lincs on 25 July 1694. This Hannah would have been of the right age to have married Carrier Thompson c1716, and to have started baptising children in Stanground in 1717, who included two Newton Thompsons and an Isaac Newton Thompson. Coincidence #2. Either Carrier was a big fan of Sir Isaac, or there was a family connection!
A lot of coincidences here. Too many to be coincidences?
A pity your Robert in Woolsthorpe didn't name any of his children Isaac, or Newton, or Carrier!
I think you're probably right. But to stand a chance of proving it you need two marriages - Robert Thompson and Mary, and Carrier Thompson and Hannah Smith. Unless someone has found a will which proves the connection, it looks to me as though all the Ancestry trees have either copied each other (undoubtedly) or someone has made the connection via the childrens' names. No-one seems to have the marriage between Carrier and Hannah, so it's an assumption that she was Smith. Wills may be the way to go.
David