Rereading the question, I would say that if you can show that a position is self-refuting, then that's pretty damning for that position. The key, however, lies in the "if you can show" bit of that claim.
I'll limit myself to just one example. There's a common refutation of hedonism that goes something like this:
- The hedonist says we just need to value enjoyment and not waste our time thinking / having values.
- aha! the hedonist is thinking / has a value.
- Ergo, the hedonist has a self-referentially incoherent view.
Despite the self-reference problem, this actually isn't a refutation of hedonism per se. The difficulties are whether or not we accept step 2 with respect to the hedonist and whether we can really attribute 1 to the hedonist. Put another way, this is a refutation of "reflective hedonism" -- in other words, you can't coherently reflect on how you should live your life and be a hedonist of the rawest sort. But does a hedonist have to even hold to 1 in accessible way?
The same sort of outcome will play out in most self-referential problems in philosophy. For instance, someone might say believing in God and believing in causality is self-referential incoherent. But most forms of theism see God as precisely that which lies outside of the system of causation and its rules.
Maybe to reword all of that and some up, self-referential is a real problem, and if you write a paper showing that some commonly held philosophical view is self-referentially incoherent, it can probably get published and would be considered "scholarly." But odds on the people who hold this view would argue against the accuracy of the self-referential incoherence by suggesting you misunderstood their view or are misrepresenting a term in it as being on a different level than where they use it.