I’m also not at all averse to synthetics, after all most perfumes are composed of synthetic materials, but I call these notes “synthetic [woody or whatever]” simply because I’ve never had this with vintages or “all-natural” perfumes. (To clarify: what I mean is that I don’t think it’s a natural-derived material that’s doing it. The word synthetic as such is not a value judgement for me.) It’s also mostly recent releases, which leads me to conclude it’s some ingredient(s) that have recently either become available, or is more popular now, or is used in higher concentrations.
Recently I tried the Matiere Premiere line and most of those fragrances I tried had a little or a lot of that unidentifiable something. A couple of them do list ambroxan, so that may be one ingredient but not necessarily the only one. (I’ve also really liked some fragrances despite them containing ambroxan, so maybe it’s about the dose.)
These days I just tend to be wary and try perfumes, especially anything with woody and musky notes, before committing.