The linguistic turn was a phenomenon of twentieth century philosophy. A main premise of the linguistic turn is that philosophical problems are caused by misunderstanding language.
This is especially true when there are conflicts between two competing philosophical "truths." Existing truths include Religion, Science, Law, Economics & Beauty. Thus, the linguistic turn becomes useful when you try to talk about two different existing truths. Talking about competing philosophical truths requires that you accurately describe the truth as understood by believers of that truth and that you not specifically advocate for one truth above another truth.
Moderns tend to think as Science and Economics as the two dominant truths but that's probably just because the last century has featured an unprecedented collaboration between the two. You would only have to go back a couple centuries to find neither truth criterion "in existence" let alone possessing a systematic accompanying philosophy. Before that time you're talking Religion, a little Law and a little Beauty as representing potential truths.
If you are going to advocate for Beauty as Truth, you need to be prepared to encounter a variety of non-believers. These range from people who actively disagree with the proposition that Beauty is Truth, to the great majority of people who don't have an opinion on the subject and don't give a shit.
Primary advocates for Beauty as Truth are often Artists- though one has to think of a specific Artist to evaluate whether that subject is important to them or whether they might perhaps believe in the primacy of Economics. The primary manifestation in the "truth" of Economics is the idea of the Market. At the same time the actual market- owing to the tremendous success the real world counterpart of the philosophy of Economics- requires the Beauty as Truth advocate to negotiate the real world Market Institutions- whatever they may be.
The danger for the Artist/Beauty as Truth advocate is that he will lack the ability to distinguish appropriate responses to Economics/the Market on both the abstract and concrete levels.
It's quite easy to imagine a scenario where an Artist's experience with Market Institutions compromises his ability to produce "authentic" Art- something a "true" Artist is presumably obsessed with maintaining. I would argue that Authenticity is derived from the sustained pursuit of Beauty as Truth by the Artist, so anything that interrupts the elaboration of that process interrupts the ability of the Artist to function.
Thus, to Artists I would counsel active, private engagement with the ideas underlying the Market (and its tremendous success vis a vis the role of Beauty in society) and a more passive but public engagement with the Institutions of the Market- recognizing their importance, but not embracing the mechanics, so as to avoid philosophical "taint" in future Artistic product.