My sons bike runs MT400's -they do not do this on his bike. Shimano make quite nice brakes, even in their lower end ranges so I would not expect this. While there is movement in the pads, the tolerances are tight enough its not usually noticeable.
One possibility, the lever is not compressed enough and the disk is moving a bit. Ultimately it does not matter if brakes don't work well with static friction or are a bit noisy - bike is stationary - so it might be as simple as there a little movement before the bite kicks in.
Other than that, the movement could be caused by only three things - loose disk rotors, loose calipers or loose axle. Given its both wheels, I consider this unlikely.
That's not much of an answer, so what can you do? If the bie shops have seen the bike , I would go with their opinion. there is unlikely to be a problem. If they have not actually inspected the bike, I would be checking the tightness of the disc and calipers.
Any chance the wrong pads are installed?