It depends on how it is transmitted. Tapeworms which are common dog or cat strays are spread by fleas. This species of flea has no interest in reptiles so tapeworms won't be an issue. Other ways of transmission of other types of worms are licking or eating the feces or feces contaminated item from an infected host (Very common); spread from mom to baby in the womb; eating a host that has the worms (ie snails, raw fish, raw meat or prey common among feral cats); and standing water that carries the parasite (ie Coccidia is very commonly transmitted this way).
So for snakes, the chances of them getting parasites from mammals is slim. Keep in mind host species matters the most: if the parasite enter the wrong host, it will usually die on its own with little side effect to the host. Your snake is most likely to get a parasite from the prey it eats.
On a side note, I used to rescue and foster kittens as well (Before I got into snakes). Most flea preventative do a fast, good job ridding most of those worms. I highly recommend Revolution for young and adult cats as it kills a wide spectrum of parasites and works within 24 hours or less. If you can get your hands on some, or at a discount, it will help greatly (Work with your rescue or local rescue. They are more open to help if you are fostering for them).
My cats sleep on the bed and couch, and my snakes hang out with me on the same bed and couch (Not at the same time). I have yet to see any ill effect or signs of illness in my snakes.
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