GREAT question! I wasn't sure myself so did some research for you and found this (website: http://water.usgs.gov/owq/FAQ.htm#Q27 :
27.Q: If the sulfur content in my well water is a little high, is it still safe to drink?
A: Sulfur is not regulated as a primary drinking-water contaminant, so there is no official level of sulfur that represents a threshold between healthy and unhealthy concentrations. Sulfur is required by all living things as part of their normal metabolism, so the body needs a certain amount of sulfur just to live. Any adverse effects of sulfur in drinking water appear to be related to the following issues: 1. Hydrogen sulfide (H2S) is sometimes present in well water. A few tenths of a milligram of hydrogen sulfide per liter can cause drinking water to have a rotten-egg odor. While unpleasant, it is not harmful to health. (See Question 20 on this web page, which discusses odor and smell.) 2. High concentrations of sulfate (SO4--) may be associated with diarrhea. For this reason, and for aesthetic reasons related to taste and odor, the Environmental Protection Agency currently has a secondary drinking-water standard of 250 milligrams per liter (mg/L) sulfate. Further information on sulfate and drinking water can be found at this web site: http://www.epa.gov/safewater/sulfate.html 3. Some waters with elevated sulfate also tend to have low pH (as in acid mine drainage). The pH of water is usually checked when well water is tested. A pH between 6.5 and 8.5 is in the range recommended by EPA. BotXXXXX XXXXXne: If you are not bothered by a rotten-egg odor, and you don't have a sulfate concentration over 250 mg/L, you should have nothing to worry about from the sulfur.
I also found contradiction in various homeopathic references I have indicating that yes, it can cause gastric upset, gum and dental disease. I guess like anything there is always two sides which is preventing me from giving you an absolute answer - which I'm sorry for. If I do come across anything else informative, or if another Specialist has input - you'll be the first to know! (Also, I have well water with moderate sulfur content - farm and house pets are very healthy!)
YEP..to all of the above. If your dogs are "farm" dogs they will do fine as well. Every now and then I have owners of cats who are on well water to use bottled water...just to help with appropriate fluid consumption. Cats can be so picky about their water source. If you have "farm" cats...there should be no problem!