Any company with an HR department is too big...
My first corporate job tangled with the HR department to get through the door... It took a year even with the engineering department VP and other engineers wanting me there to get an entry level engineering technician job... I was promoted to senior design engineer in about 2-1/2 years with no degree or further education after I was finally hired... I quit just short of 5 years and became a consultant to them an others and about year after that started my own engineering company. We've been manufacturing our own products for about 25 years now...
For my current job, I transfered over from another department. Because I wasn't a "diversity hire", and because they were behind on their "diversity targets", my manager had to go have lunch with the VP that runs the department to make the case why they should make an exception.
I've worked with people of all sorts of races, colors,creeds, religions - I don't care about those things and can't imagine discriminating against someone because of those characteristics. But to turn away qualified candidates so you can chase a vanishingly small pool of "diversity candidates" is insane.