May Thorseth's contribution to the collection is a piece on ethical pluralism, which she presents as a more substantive alternative to relativism. I agree that distinguishing the two positions is a very worthwhile thing to do, but here I will quickly argue that teasing pluralism apart from relativism is probably harder than Thorseth's piece makes out. Like the other pieces in the collection, this one is very compressed and covers a lot of ground quickly, and I don't imagine it's meant as the least word on the subject. Still, as presented I believe there is a form of relativism which can manage everything Thorseth gives as a reason to prefer pluralism. Then I make a suggestion which I hope can serve as a way to pin down the difference Thorseth is gesturing at.
Her case, following Charles Taylor, is that a purely formal approach such as relativism can't pick out the goods which are connected to import-attributing feelings, for which only a substantive engagement with a position can suffice. I will make the rather obvious reply that you can conceive of a relativism which is up to task, one of the form 'it is right for X to pursue those goods which promote import-attributing features'. Because this is really boring I want to instead say something about why I think it is a mistake to place too much weight on what someone might feel when you're trying to pin down concrete goods.
The idea behind import-attributing feelings is that not everything a person does is something they consider a matter of integrity: people often feel that it is of critical importance that they get to practice their religion or live a particular lifestyle, while it is decidedly odd for someone to tie how well their life is going to whether they around trees clockwise. The challenge for relativism is supposed to be that, from all the candidate goods available, a purely formal approach can't see whether some good is the target of import-attributing feelings. For instance, cultural membership is very important for many people, but there are others who attach no importance to it, so a relativism which makes cultural membership be the deciding factor in what is and isn't moral is inappropriate.
However, there is nothing that stops a relativism which determines rightness by way of which goods are the targets of import-attributing feelings. It would go something like: if X is the target of an import-attributing feeling of A's, then it is right for A to pursue X - let's call this relativism from import attribution (RIA). This is no different in form to the paradigmatically relativist position 'if members of A's culture typically pursues X, then it is right for A to pursue X'. You could complain that you can't determine what those feelings target without a substantial engagement, but nor could you see what someone's culture membership is. Furthermore, there is something right about RIA: cultural membership is a paradigmatic concern of relativism, but only because people typically consider it to be a central feature of your identity, and likewise for other candidates of the formal property that the relativism concerns itself with.
Concentrating on feelings leaves the door open for relativism, because feelings are feelings about things, that is, they are higher-order properties which can attach in various ways to more immediate goods. The problem, which RIA shares, is that such feelings can attach to almost anything, leading to Phillipa Foot's complaint that even a sophisticated relativism like Richard Hare's can lead to such absurdities as irresolvable moral disagreements about running around trees clockwise. To prevent this, there needs to be some restrictions on what could rightly be a target of such feelings, that is, propriety conditions, like which Foot's own 'natural goodness' account tries to deliver. However, doing so is very difficult, and Thorseth makes no attempt to do so, so pluralism as she presents it is in the same muddle as RIA because anything could potentially count among the variety of goods.
Nonetheless, we can establish that there must be such propriety conditions through the use of the Euthyphro problem, much like I presented in an earlier post (such uses of the Euthyphro problem are something I've written about and continue to work on). The dilemma goes as follows: either the feelings are just a way to know what goods are involved (how Thorseth, Taylor et al present it), or being the target of such a feeling is the good-making feature (as RIA has it); but it can't be a good-making feature, because then anything whatsover can be an ethical good, such as looking at rabbits under moonlight (another example of Foot's), which is just absurd; thus, the targets of these feelings are good independently of the feelings; thus, those feelings are only appropriate when they rightly target those things which are good. And now we have the task laid out clearly: to identify what the things are to which one rightly assign importance.