In the UK we never use cups, only metric (for most recipes nowadays) or imperial measures (pounds, ounces, pints, tablespoons etc.). Note that the cup measures used in NZ and Australia are slightly different from the ones used in the US, also the Australian tablespoon is bigger than the one used elsewhere. Generally you are safe enough using metric measures everywhere in the world except the US, where you must use US measures - cups for volumes less than a pint, pounds and ounces for weights. Volume measures would be used for liquids and powders, but also 'flowing' solids such as rice, corn (grains) or sweetcorn niblets; you could imaginably measure chopped mushrooms this way, but certainly not whole ones. The split between US (conservative) and the rest of the world (metric) applies to some other measures too, not just cooking.

In New Zealand, an entirely metric country, we use cups in cooking. However for mushrooms this is a bit strange. Perhaps just state roughly how many mushrooms are needed or use a weight recommendation?

This is a little bit regional. In metric countries you won't use cups. In imperial countries (US and Britain for some things) you will, but normally only for items you're able to scoop into a cup, as it is a measurement of volume. So saying 2 cups of water is ok, 2 cups of corn is probably ok (it they are loose) but 2 cups of cheese is probably not (assuming it is a block). Here you would typically measure by weight, and if you wanted to stay in imperial you would measure by lbs or Oz. You could switch to metric and say gram but then why not say millilitre instead of cup and keep everything in metric.