no you are not being unreasonable and yes it is normal.
it costs ALOT of money to shelter an animal.
right now, shelters are so overwhelmed with dogs and cats and other animals.
yet their funds are extremly low, lower than they have been in decades. We have had to totally turn off the electricity in our dog kennels
if people do not donate money to local shelters, those shelters have no money, they operate 100% on donations from the public.
right now, people are losing homes and jobs and donating is the last thing on their minds, which is perfectly understandable, but that means local non profits suffer and the services they offer are less and less.
it sucks because animals suffer but its unavoidable.
many of these shelters do not own the vets they use, the vet has their own practice and donates their services to the shelter, either for free or at a discounted price.
the vet is not getting clients right now either so they possibly can not afford to give these services for free or discounted prices, so they charge more which costs the shelter more ... that money has to come from somewhere ...
did you make it very very clear that she is not your dog and that there is no way you can keep her, you have no ability to keep her, and you are trying to do what is right by finding her a home? like really really stress that as firmly as you can without being rude.
they dont like to charge people like this, trust me, ive worked in admissions and we hate having to do it, we know people cant pay it and thsoe thn can dont ussually want to.
maybe you could call various vet offices and talk to them, many vets are willing to take in strays.
or try to just find her a home ....