Minimalism is the antithesis to clutter.
A coaster does not necessarily violate minimalism, but true minimalism would not need a coaster because surfaces would not be harmed by a drink with condensation. So if your coffee table was wood, a coaster is compliant but a glass/concrete/polymer coffee table or putting a glass pane on top of the wood coffee table is better. The coaster is unnecessary because the entire table is a coaster.
People who use knickknacks as decoration have a need to fill space just for the sake of having something there. Minimalism does not create an unnecessary space to be filled. Putting tables/shelves/bookcases with no purpose but to fill a space is not minimalism. Having a table to put a lamp on, a shelf to hold plants, or a bookcase filled with books can be minimalist. Buying a table to put in a "vacant" space next to the bookcase so you have a place to put a ceramic chicken you saw at a resale shop is clutter and not minimalist.
Lack of color is a "minimalist" interior design concept trend. Minimalism is not inherently nothing but white, black, and grey. You can have a minimalist space that has every color of the rainbow. Purple walls, blue area rug, red coffe table, yellow lamps, orange couch, and green plants would all fall under minimalism but the indigo sign that says "family" violates the core concept of minimalism.