This MWE does not compile:

\documentclass{article}
\usepackage{fancyvrb}
\usepackage{tabu}
\begin{document}
\begin{tabu*}to\linewidth{|XX|}
A&
\begin{Verbatim}[commandchars=\\\{\}]
And this is a complete
Verbatim environment
\end{Verbatim}
\\
\end{tabu*}
\end{document}

That was already the case with TL2017. I read the manual but not the source code. Ah, I looked a bit now after examining a trace. I see in particular

\iftabuscantokens \endlinechar=10 \obeyspaces \fi

on line 1134 of the code in tabu.pdf, although I did not check if that line is really relevant it immediately brings to mind the well-known problem of scantokens with an active space.

I see now tabu's author is aware, as later on there is section "Compatibility with the fancyvrb package" in commented source code, and he adapts the fancyvrb end-check via \tabu@fancyvrb code. (lines 1912ff)

Thus this does not work if the \ has its native catcode. This is source of problem, which hence is deeply coded into tabu code: there is no provision for it to work with a Verbatim configured à la "alltt"".

Hence raising this issue here, to at least make it clear in the manual, or to handle it as a feature request.