Yes, the problem is that _ has two meanings here: in Markdown it indicates italics:

_this_ gives _this_

while in MathJax it indicates a subscript:

\$$x_2\$$ gives \$$x_2\$$

Since Markdown is more fundamental here than MathJax, there's always the possibility that MathJax commands will be interpreted as Markdown. What puzzles me is how often they _aren't_. But you can avoid the problem by using \_, as Dan explains.

The conflict seems to happen when you include text in MathJax. Let's see if I can find a minimal example:

\$$\texttt{C}_1 \to \texttt{C}_2 \$$

gives

\$$\texttt{C}_1 \to \texttt{C}_2 \$$

No problem there!

\$$\mathrm{C}_1 \to \mathrm{C}_2 \$$

gives

\$$\mathrm{C}_1 \to \mathrm{C}_2 \$$

No problem there either!

But this is enough to cause a problem - you'll see italics appearing after one of the underscores:

$\texttt{CategoryToPreorder}(\mathrm{Obj}( \mathcal{C}_1 ), \mathrm{Obj}(\mathcal{C}_2), \mathrm{Obj}(\mathcal{C}_\leq),$

gives

$\texttt{CategoryToPreorder}(\mathrm{Obj}( \mathcal{C}_1 ), \mathrm{Obj}(\mathcal{C}_2), \mathrm{Obj}(\mathcal{C}_\leq),$