I wear mostly wool for all layer and articles of clothing but personally for sleeping I use cotton sheets and blankets. I have a couple of Bates Mill Store (basically New England Faribault Mill equivalent) cotton weave blankets and they are great for winter and summer. I would be hesitant to use virgin wool as a single layer next to skin, as much as they claim it to be super soft I’ve never had virgin wool that wasn’t mildly irritating to skin. If I did go wool route I’d look for Merino only, I don’t personally have experience with that particular blanket though so just my opinion! More on reddit.com

Fun fact about Boll and Branch: they advertise on Tucker Carlson's show. He is a white supremacist. Don't buy Boll and Branch sheets unless you are okay with them actively aligning their brand with white supremacy. More on reddit.com

Muslin blankets (sometimes also called “gauze” or “matelasse”) are very light and soft. More on reddit.com

I can't give you specific recommendations as I tend to buy bedding from places like HomeGoods and in the past Tuesday Morning (RIP) but as to your cat question, yes your cat's claws can snag on them if they make biscuits as they say. Depends on the cat honestly. I've got one that LOVES waffle and knit weave cotton and will spend ten plus minutes just kneading the blanket which leads inevitably to snags. My other cats could care less and just do a little circle and plop down without getting their paws and claws involved. More on reddit.com