I read your post a few days ago and have been pondering what I would do since I have a beach house and rent to an upscale clientel.  So far, I have not encountered the problem because we use only white linens and with white linens the spray on tanning will wash out with soap and bleach.  If you use colored linens it may be another story.  We went all white for the same reason hotels do.  They can be washed with hot water, strong detergents and bleach.  Your other options would be to build in the cost of replacemnt linens into your price and toss them and replace them as needed or to include notice in your contract that use of spray on tanning products may incur a linen replacement charge (not as friendly and may be problematic).

Perhaps a friendly warning to guests about products that may stain sheets and require you to discard them and charge the guest is in order?

I rent my summer beach home and have never encountered this problem (and hope not to). 

If this has happened multiple times, I would warn your guests, in the most friendly terms, about products that could stain the linens and therefore should be avoided during their stay.  You might indicate you wll  charge their security deposit for any linens that can not be cleaned and must be discarded.   

The you must decide, if it happends, if you will actually charge or let it go.  As others have mentioned, it's often best to build wear and tear such as linens into your rental rates and avoid charging the guests' security deposits. 

I agree that white sheets are best for ease of cleaning, and a fresh appearance.  There is a clean and crisp appearance to a white sheet that colors can't achieve, in my opinion.  

Best of luck in sorting this out!