Redefining commands always carries some risks, if that command is used by other ones. This is one case.
There's no general rule, unfortunately, for telling whether a redefinition can harm other commands. You've found that
\triangleleft is used by
\bowtie and it's almost obvious that there's a problem, because
\bowtie is defined by
fontmath.ltx. What you should do is thus
\bowtie will use the "uncolored" triangle.
However, I don't recommend this path. Rather, define a new command for the green triangle, reflecting its intended meaning.
If the green triangle left is to be used in the same way as the black one, I suggest to declare it as a binary operation (
\triangleleft is a binary relation symbol):