Will installing HomeBoost or TapBoost reduce the pressure and flow for my neighbours?

Having a mains water booster pump does not affect the water pressure next door. If a property has a pump installed, they are not actually siphoning your supply, just using a pump to increase their own water pressure. When the pump is running and using water, it may cause a slight drop in pressure for the neighbour, but so small, its barely noticeable if at all.