I can only guess that it's because of the variability of dialects in Faroese, they can be quite different and often there are stories of ridicule from other Faroese speakers from the other side of the country (even though it's so close) based on the difference of the dialect. I think it's possible that the author has possibility got the pronunciation my book marks as belonging to the younger generation, with a fricativised [ɻ], and I understand the logic in using that symbol because IPA doesn't make a distinction between the sound [ɻ] as an approximant (which it is usually considered to be) or as a more hissy fricative, so the closest more regular sound in IPA for this sound is exactly [ʃ].
But that's just a half-educated guess. Some books don't even use [ʂ] but just use [s] instead (when [rs] appear), so the symbols used in representing pronunciation aren't really standardised, that and the variability of dialect pronunciation leads to a messy situation of sound representation with different symbols in different books in different websites. In essence though, we're splitting hairs about what symbol should be used, the symbol would be enough for a speaker to understand you, I'd assume.
Edit: Yeah I've gone over an audio lesson for it and can hear the pronunciations, I honestly don't think I could tell the phonetic differences apart from (loose ideals of) and a [ʃ] or a fricativised [ɻ] OR [ɹ]. This is what you'd probably tweak to perfection when you can communicate in the language. They aren't really sounds that differ in any significant way (at least for me), so I wouldn't be put off or confused unnecessarily by this. I know my Icelandic pronunciation isn't perfect, but I'm working towards it. Other people can go ahead and do all sorts of Rs, even without trilling them, but it doesn't impede communication and with practice comes perfection. It's like starting with English and trying to grasp aspirated and unaspirated voiceless plosives, people can be considered virtually bilingual and have no idea about the difference, and the difference phonetically is much more significant than between these symbols we're talking about here.
My only advice would not be to blast out the sounds, have a relatively weak pronunciation of them but capture the essence of the sound. Don't start saying "Shhh!"-like sounds when you just mean to have some hissy R-sounds. If you do that I can't imagine you running into (m)any problems.
