What you want to do is possible, but typically impractical. In order to do it right, you would need to do the following:

1. Purchase and install a commercial-sized RO.
2. Purchase and install a large surge tank and, quite probably, a booster pump.
3. Replumb all of the lines through which you wish to run RO water in plastic pipe
4. Locate and purchase faucets that can handle the RO water (or install separate RO faucets at each location)
5. Locate, purchase, and install a new hot water heater that can handle the RO water (this one will be difficult)
6. Probably do a lot of replumbing to separate the RO and soft water systems.

Alternately, for hot RO water, you can purchase a small water heater with a stainless steel tank suitable for RO water use.

A better option, if you want nitrates removed from all, or most, of your water, is to install a nitrate-selective anion exchange bed. If you have hardness higher than 4 gpg, particulates or iron, those would need to be removed prior to nitrate removal. You need a water treatment rep that knows what s/he it doing as anion resins are much lower density than softener (cation) resins, require lower salt concentrations and backwash flow rates and generally make equipment sizing more complicated. When sized and set up correctly they work very well. Do not use a mixed bed for this applicaton (cation and anion mixed, which some companies call a "nitrate-eater" softeners. Mixed beds are great for polishing out ppm/ppb levels of contaminants but are problematic for bulk removal from raw water.

RO water is aggressive. Water is a universal solvent and it doesn't like not having any dissolved solids and for that reason I don't think you would put it through a water heater or in contact with a lot of metal. You would still have a special faucet in the bathroom, for example. Nitrates are not absorbed through the skin, so there isn't a benefit to filtering more than your drinking water.

Is the water pressure decent, Fred?

Our well water is naturally soft, it's just the nitrates. In fact, the hardness it does have comes from the calcite in the neutralizer (the natural pH is in the 5's and corrodes copper).

Can you still bypass it for things like the outside spigot?

"Is the water pressure decent, Fred?" Yes. The water pressure has nothing to do with the RO system. The RO dumps water into a cistern. Then, the pump in the cistern feeds the house. The pressure is as good as the pump used. The pumps are usually sized by volume and vertical lift required, so it will usually be smaller than the well pump. A constant pressure pump is a nice upgrade.

Can you still bypass it for things like the outside spigot? The house was built with this in mind. There is a manifold at the pressure tank that allows switching from RO to well water. There are also two hose bibs on each end of the house. One is permanently untreated well water, and the other is on the side of the system that can be switched.

OK, good info.

So, I wasn’t aware of the nitrate-selective anion exchange bed as an option.

We will stay put for now, but I was curious what options exist. It would make little sense to use the treated water for the outside spigot, for a couple reasons…one, I water my veggie garden, and even if I switch to drip irrigation, we’re talking hundreds of gallons in one sitting, which would empty a cistern and/or put a lot of use into an RO system…when soft water that contains some nitrates is probably GOOD for plants. Same thing for filling a pool, or washing the car, or running the pressure washer – it seems silly to use RO or treated water for those purposes.

That’s why a bypass makes sense.

Doesn’t RO Make the water so soft and acidic it will corrode copper? We have a neutralizer because our water is so soft and acidic to begin with. Or, are you better off using CPVC or something like PEX with RO water anyway?

"Doesn’t RO Make the water so soft and acidic it will corrode copper?"

Not necessarily. It is a matter of degrees (ie, if the earth were to get 2" closer to the sun, that is 92 million miles away each year, should we make a big deal out of it?) and contributing factors (ie, everything causes cancer in laboratory animals, does not mean the same will happen to you). An RO basically turns normal water into rain water. Would you be worried about rain water? This is more theory than reality. Even a copper roof will not gain a patinna over time without impurities in the air. That is why coastal roofs turn green faster, and wood siding greys faster than in a salt free, smog free area. The RO takes out impurities. Nitrates also cause corrosion. Would you rather have the corrosion because of nitrates, or pure water?

"We have a neutralizer because our water is so soft and acidic to begin with. Or, are you better off using CPVC or something like PEX with RO water anyway?"

You would be better off with PEX just because of the water you have NOW. The degree of "better off" would probably not change just because you run the water through an RO. It is still not an exact science, and the consensus is more that it takes a rather exact ratio of a combination of things to cause a problem. My parent's pipes are as good as new after 35 years.

http://www.fwr.org/copper.pdf

There is an extremely flawed post on GW that might be perpetuating this. The strap used for the "test" was not even copper, just a coating on the outside, which cause a reaction for a totally different reason.

http://ths.gardenweb.com/discussions/2521618/does-reverse-osmosis-water-corrode-copper-plumbing-the-answer

They essentially made a battery. Those coated straps should not even be used in a humid crawl space.

There may be reason to be concerned, but the only way to know for sure what will happen to your system, is to put it in, and then test the water. What may be a more pertinent concern is what type solder was used.

http://www.water-research.net/index.php/drinking-water-issues-corrosive-water-lead-copper-aluminum-zinc-and-more