DeclareMathSymbol{j}{mathalpha}{operators}{`j}

documentclass{article}
usepackage{amsmath}
RequirePackage{fontspec}
RequirePackage{unicode-math}

DeclareMathSymbol{j}{mathalpha}{operators}{`j}

begin{document}

begin{equation}
j ~~text{is not}~~ mathrm{j}
end{equation}

end{document}

documentclass{article}
usepackage{amsmath}
RequirePackage{fontspec}
RequirePackage{unicode-math}

setmainfont{Minion Pro}
setmathfont{MnSymbol}
setmathfont[range=mathup/{num,latin,Latin,greek,Greek}]{Minion Pro}
setmathfont[range=mathbfup/{num,latin,Latin,greek,Greek}]{MinionPro-Bold}
setmathfont[range=mathit/{num,latin,Latin,greek,Greek}]{MinionPro-It}
setmathfont[range=mathbfit/{num,latin,Latin,greek,Greek}]{MinionPro-BoldIt}
setmathfont[range=mathscr,StylisticSet={1}]{XITS Math}
setmathrm{Minion Pro}

DeclareMathSymbol{j}{mathalpha}{operators}{`j}

begin{document}

begin{equation}
j ~~text{is not}~~ mathrm{j}
end{equation}
But actually $j$ is not there at all.

end{document}

setmathfont[range={"006A} ]{Minion Pro}