Go here to find a list in NJ.

Upvoting since I have this issue as well (in Monmouth County). They have Greenmarkets on specific weekend days in NYC that have drop off for textiles, but have yet to find something equivalent in NJ.

https://www.helpsy.co/find-a-bin

Thank you, but the big issues is that these (and almost all) donation bins are for clothes and shoes that can be washed and then given to another person to wear.

I have a bag of pants with HUGE rips; shirts that were for yard work and are now nearly destroyed, and so on. If one of these donation companies sees tattered clothes they will just chuck ‘em— I am hoping to find a group specifically focused on repurposing textiles that are no longer functional.

I understand. I'm not certain how this particular bin works as it is in the Homeless Solution's parking lot in Morristown and they show this bin to make clothing donations (to be given to another person). In the Helpsy about me section:

>95% of what we collect is reused, upcycled, or recycled. 50% is reusable, 45% is recyclable. It is first sorted by our partners and divided into grades. The higher grades are resold to thrift stores in North America and other secondhand markets around the world. The lower grades get turned into rags for industrial use or things like stuffing and insulation.

The link from scrapmonster may be more in line with what you're looking for.

My understanding is that most of the "donation" bins that borrow a charitable organization's logo are actually operated a by for-profit company that sells everything to recyclers, and pays the organization a fee to use their logo.

Almost any animal shelter will accept them. I do the same thing with old towels and blankets.