You can’t generalize about rescue organizations from contact or lack of contact from just one of them.
Drop them off at a shelter.
We get a fair amount of “stuff“ from people, and it’s good, and we generally make use of it. We are very aware of the public relations aspect of accepting donations no matter what the donations are. We take them with a smile and a “thankyou” and an offer of a tax letter.
When our rescue director was hit by a car,I stepped in to do some of the grunt work. One of the first things DH and I had to do was to go to someone’s house who was moving. They had saved tons and tons of stuff for what they thought would be useful for dog rescue such as bedsheets, blankets, T-shirts, as well as items made for dogs. We filled the entire SUV. That was a bit much and it took me a week to sort through it, some of it went in the trash.