On reference I agree with Yahadreas that reference is metaphysically or ontologically non-committal. This is obvious form the fact that we have (1) actual linguistic markers for talking about non-actual situations even when we're anchored to actual discourse -- linguists call this modality -- and (2) methods of shifting the basis for discourse altogether away from actuality -- fictional discourse. The point is not simply that we can talk about things we would independently consider to have no status as 'real' in the sense the realist is interested in it, but that, in such cases, language seems not to change in its behaviors at all. To put it simply, language works exactly the same way whether you're in the Matrix or not. It seems completely blind to such questions.
Insofar as linguistic 'anti-realism' is a merely negative thesis, then, that the behavior of language provides support against the realist's claims about how language somehow secures or props up reality, I would say that these facts are good grounds for linguistic anti-realism. Certainly, one is not committed to anything like SX's claim, whatever it might mean: the question of whether language itself treats linguistic structures on a par with non-linguistic ones is an interesting one. In some ways, I think it does: all languages have mention mechanisms, for example, that effectively give speakers the ability to form quasi-proper names out of words just by the fact of those words' existence (what we in philosophical discourse use quotations marks to mark), and so do take words to be 'things' as much as they take anything else to be 'things.' But in other ways, language seems curiously blind to itself: it lacks mechanisms for describing its own mechanisms, outside of formal linguistics, where we must use the medium of models. For example, we seem to be unable in natural language to self-reference our own speech acts except in certain 'performative' constructions, which in English often license the adverb 'hereby.' Thus you can say, 'I [hereby] challenge you,' but you can't answer a question like, 'What are you doing?' with 'I'm answering your question.' That is, the descriptive assertion is incapable of itself describing what it is doing; it is forcibly interpreted as a description of something else.
I'm not quite sure on this subject, but my inclination now is to think that because ontology or metaphysics are themselves discursive practices, and the medium they're forced to employ itself refuses to validate the very theses that are made in that medium, there is a sort of incoherence to questions of ontology and metaphysics. Or, at the very least, to the extent one has an ontology or metaphysics, it must be non-linguistic (and I do not rule out that possibility) and the best language could do to illustrate it would be to 'lead people' to that non-linguistic understanding rather than straightforwardly describing 'the way things really are.'