This is pretty much a '17 version of this question, since the solution provided does not work (anymore) in this case and neither does any of these other answers, because tabu has its own rules.
The syntax highlighting works, using mintinline in the cell correctly highlights the code. There are no visible problems, it just throws the following error:
Package minted Error: Missing Pygments output; \inputminted wasor may be using frozencache with a missing file. \end{tabu}
Here is a short MWE and the compilation result:
\documentclass[preview]{standalone}
\usepackage{tabu,minted}
\begin{document}
\mintinline{html}{<p>This works</p>}
\begin{table}[htb]
\centering
\begin{tabu} to \linewidth {l | X[c] | c}
Col1 & Col2 & Col3 \\
\hline
A & \mintinline{html}{<p>This doesn't</p>} & B \\
C & D & E \\
\end{tabu}
\caption{MWE Table}
\label{tbl:table}
\end{table}
\end{document}
Applying the fix from the first linked answer does not work and does not alter the given error message. Other than that, I did not find anything helpful in neither the tabu nor the minted documentation.

tabudocumentation, the command\tabuDisableCommandsdoes "change the definition of some commands during the trial loops", which you are using to replace the meaning of\mintinlineto a detokenized typewriter-text version. Am I correct in assuming that the trial runs are used to determine the column width and thustabuis now using a less complicated macro for these runs to avoid the error, only applying syntax highlighting in the final run? – Big-Blue May 28 '17 at 13:00tabuarise in the future, I now know of a possible way to handle them. – Big-Blue May 28 '17 at 13:15