You'd be surprised at what relationships might exist.
I used to work for a well-known manufacturer of window air-conditioners.
Although we were not a direct military contractor, we routinely shipped a small (but lucrative) quantity of the crucial "guts" of the compressor we made to a smaller company that "refined" them to mil-spec standards for quality and reliablity. Because of our unique design, it became the preferred component for the air-conditioning in the cockpits of one of our jet fighters.
I would guess that some of the pumps that Maytag makes for their washers/dishwashers may have a similar application. But who knows? Domestic appliance manufacturers make a helluva lot of different components that could find use in military equipment. It's not exotic stuff, but the military needs it just the same.
Maybe. But there is no relation between Maytag Aircraft and Maytag.
Now that that inconvenient fact is out of the way, you could just as easily argue that a manufacturer of ping-pong balls, through some special process it has developed, is also a national security concern. Where does it stop?