The problem soap was B&M's Passiflora. There is a list of ingredients here: Barrister and Mann Passiflora Shaving Soap – ItalianBarber - https://www.italianbarber.com/collections/creams-soaps/products/barrister-and-mann-passiflora-shaving-soapThe scent is medium-high strength for a soap, I would say. After all, you’re buying Acqua di Parma for the Colonia scent, as well as expecting it has highest quality ingredients. But of course it’s a shaving cream and the fragrance is not nearly as strong or long-lasting as in other products. If fragranced soaps can bother your skin then I guess this one isn’t for you - and not worth the risk at that price unless you had tested a small amount on your skin. Of course Acqua di Parma (LVMH) has the resources to test their products thoroughly, which small soap makers cannot, so there’s that as a counter point.
I wonder if you could narrow down what scent components cause problems for you. Which B&M soap was it? It must surely be a strong reaction to have such an effect, and I would think normally B&M soaps are safer than most. You are right to be wary. Some guys here are pretty knowledgeable about ingredients and the most likely offenders within a particular product.
I do find, by the way, that the AdP aftershave products are as good for the skin as the absolute best products I’ve used. I like the Colonia Lozione best, but they’re all great and make my skin feel amazing. But they are all strongly (but tastefully) scented, for sure.