Can I exclude products from the Free Shipping minimum order? (FSB)

Unfortunately this is not possible. The Free Shipping Bar checks the total value of the cart, so anything inside is counted.

The only exception is products that do not require shipping, such as digital products or gift cards.  If you subscribe to the Premium plan, you can select the Only target products that requires shipping (e.g. exclude digital products, gift cards) product targeting option and these products will be excluded.