Are rescue shelters making it too hard to adopt a pet?

In my opinion, they don't. I'm from the Philippines, and I used to volunteer for two animal shelters here. They have a very strict criteria for adoption which involves visits, interviews, and mandatory vet check-ups.

I don't think that animal shelters are making it too hard in a sense that they are curtailing people's rights to own pets. They just want to assure that the animals will live good lives. It is important to note that rescued animals are often abandoned or abused. Not checking the background of their new family might make the animals' lives harder.

Anyway, don't get discouraged. Continue visiting local animal shelters for you might find your perfect companion there!