As far as I know and seen, there is no specific dress code for visiting Montserrat. However, for the Abbey of Our Lady, you should wear clothing that covers your shoulders and knees: no short shorts; no tank tops; no mini skirts and the like. You may be asked to leave if considered not appropriately dressed. Use comfortable shoes as a visit here involves a lot of walking. Wear layers as you can then easily climatise and take a sweater along as the temperature drops in the mountain by a few degrees.