A lot of the LaTeX options do not work in MATLAB because many of the font options are not supported.
That aside, use \it to begin the italicized part and \rm to end it —
ax2 = axes;
plot(ax2, 1:3, [2.1 5.1 4.1])
% xlabel(ax2, '{\fontfamily{cmss}\selectfont Chord $\mathsf{c/R_p} \, \textsf[-]$}', 'Interpreter', 'latex');
xlabel(ax2, '{Chord $\it{c/R_p} \ [-]\rm$}', 'Interpreter', 'latex');
That works, except for the [—] part. It may not be possible to make that work as well. (The font is not sans-serif as well here. Nevertheless, italicising only a part of the string works as intended.)
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