Challenging traditions isn't exclusive to "the left" or "the right"
Not exclusive, perhaps, but as it's one of the differences that defines them, it's certainly massively biased towards "the left".
"The right" is in part defined by its conservatism, which actually
means the defence of tradition. Challenging traditions us, by definition, the exact opposite of conservatism, and therefore is one of the the aims of "the left", and is one of the things "the right" are typically fighting against.
If what you're saying is that even people on "the left" occasionally take a conservative stance on things that traditionally benefit them, then you're right, but by doing so they are no longer acting in the ways that normally define them as "the left".
If a Broncos fan is cheering for the Titans to win, because a Titans victory over the Panthers would put the Broncos into first place in the league, that doesn't make him a Titans fan.