Add a flapper inlet (Like this:
Link ) to the pipe, as close to the intake at the wall as possible. It should be very easy to open, like less than 3 pounds draw.
Once that is done, see if you can isolate the furnace intake (or build a firebox around it) and draft the intake lines directly to the box. The water heater shouldn't draw nearly as much air but you can do the same to it.
I would NOT cut off the supply air permanently or manually, as the house probably has Tyvek or spray foam, and the installers weren't comfortable with the negative pressures the furnace generated.
What you are trying to solve is (1) Free-flow of air into the basement when IT IS needed through the pipes- but it is mixing with the conditioned space, (2) air exchange inside-and-out
through the relief ductwork when it isn't needed (its completely normal to have constant pressure variations in buildings), and (3) the fact that they used a typical furnace but (obviously) noticed that it created too much negative pressure for the house.
(1) You want to isolate the pathway to only go to the furnace, (2) you need to prevent constant air exchanges and direct the air direction and (3) They added that relief ductwork on purpose... It would have been great if they finished the job with controlled intake but apparently they considered the basement 'unconditioned' and used the whole room as an air exchange from outside to the furnace.
The furnace box (if possible to add) needs to isolate the furnace to its own air space, and run the external intake directly into it. The house exchange air intake (hopefully) is on another floor and is already ducted into the basement and directly into the furnace, which means you shouldn't have to worry about it.
Also, get carbon monoxide and NG detectors with battery backup. I have these: "Nighthawk Plug-in Carbon Monoxide & Explosive Gas Alarm with Digital Display KN-COEG-3"
https://smile.amazon.com/gp/product/B0002EVNJ6/ref=oh_aui_search_asin_title?ie=UTF8&psc=1