If she rescued it then it is her cat, her responsibility..

Put your foot down. Help her out even. If she's the type who won't do research to find a cheap place, do it for her. Search for low cost spay/neuter clinics in your city. A quick google search is all you need. Then pick the cheapest place after looking them over.

Tell your friend where to take her and even that you will make the appointment if she likes. Otherwise, the cat needs to find a new home.

You don't need to put up with that.