This question keeps getting more and more complicated every time I jump down the rabbit hole looking for clarification. So for funsies, let me tell you all what I have found since the last time I looked! Just a warning, this will be long (and boring) for many, so please just skip if this doesn't interest you

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As some have said,
if it fell strictly under "bartering" rules then it technically
would appear to be taxable. But it would be taxable whether you swapped with a third party company or
DVC or Interval International as any of the companies would be acting as a barter exchange or barter club where they use
credits or
points for members to swap for other items/services. This sounds a lot like DVC swaps whether third party (dollar credits) or first party (points), and there are no different rules for third party or first party items swapped in a barter exchange. So it doesn't matter if you are using a form of dollar credits like the third party or a set of points (vacation club points to reservation points) like DVC themselves. None of that exempts you from being taxable as a barter exchange.
However barter exchanges or clubs are
required to send a 1099 to the user of the exchange and report it to the IRS, which leads me to believe that DVC and the third party swaps are NOT considering themselves being used as a barter exchange or barter club. Otherwise they would be very easy targets for the IRS to come down on them and make some easy money from every point swap (and we now know that number is around 20% of all DVC points in any given year!)
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So they must be using some other parts of the tax code rules instead. One of the closest things I can compare is trading in a car (and I have brought this example up before). You are trading in a car as part of the payment for a new car (possibly with additional cash if the new car or used car you are trading for is worth more than your trade in). I think this is still a helpful comparison now, even though they are not exactly the same.
They removed the like kind exchange provisions years ago for everything except "real property" for businesses. All personal property has been removed from those exceptions, so the car trade ins are not using that.
From everything I have seen it appears that they are just using standard sale/barter rules and that they are just assuming that your car is trading in for less than you bought it for since cars depreciate so quickly, and selling personal property at a loss is not a tax deducible loss (or we would all be selling our old junk for pennies lol). But if you actually were to trade in or sell your car for more than you paid for it originally it
would result in a capital gain and that increase would be taxable, it is just very rare and you would have to self report it.
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Now back to DVC. If you sell your contract for more than you bought it for, you would owe taxes on the gains of course. But rentals/usage are a bit trickier. If you rent out a reservation and receive cash then it appears you need to report those gains, minus your costs. But allowing
the use of your timeshare appears to follow slightly different rules than renting your reservation for cash/selling your contract.
The easiest one to see is with donations as it is spelled out clearly and specifically. If you donate your reservation/points to a charity, you specifically are NOT allowed a tax deduction, regardless of how much the reservation is worth or how much it "sells" for at a charity auction. But if you were to rent out the reservation for cash and then donate that cash then you would pay tax on your just your gains, but then get a tax deduction based on the entire amount (your cost+your gains). So it would be better to rent then donate in this case instead of just donating the reservation.
https://www.redweek.com/resources/articles/donating-timeshare-to-charity#:~:text=The tax law specifically prohibits,Aspects of Renting Your Timeshare
"
Someone contemplating a timeshare donation with a resulting tax benefit should ensure that it's the ownership of the week that is to be donated. The tax law specifically prohibits a tax deduction for donating the use of a week (e.g., donating this year's week) to charity."
But this just goes to show that there are ways in which they treat transferring the use of a week very differently from transferring the entire ownership of the deed or even renting a reservation for cash. So transferring/bartering with (aka transferring a partial interest in) the use of a time share week may not actually be taxed in the same way vs if you receive cash in exchange.
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All of that being said I don't know if the companies are actually using something related to this info as a deciding factor in the taxability of swaps at all, I just thought this was interesting info that I had found. And I am not your tax attorney, yada yada, etc.
In the end, if all of the industry "experts" and DVC themselves are treating it as nontaxable and even saying that there is a tax benefit to doing it, I am not going to argue with them about it

(even if they don't point to the exact tax code as their reasoning why. I wouldn't want to pay more taxes than I am required to after all.
And I am not going to get started on how ridiculous enforcing every transaction in the country as bartering would be. Technically if a friend and I go out to eat and swap half of our meals or buy apps to share then that would need to be reported as the swap would be over $1 in value

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And lastly I did see some info about the Augusta rule possibly being allowed specifically on deeded time shares and that you may be able to rent tax free (even for cash!) for up to 14 days of a stay per year as long as you
also stayed there for at least 14 days that same year.