black fabric or material that is really non-reflective

Cinefoil is the typical solution for photographic and film use. The generic name is “black foil” because “Cinefoil” is a brand name.

The usual photography suspects - materials such as Duvetyne - are meant for reflection control on-set or as backgrounds. The fabric is dark enough that you can use them in conjunction with the inverse square law to pretty much ensure that local lights (and reflections from objects on set) will be well below "exposure black" by the time (or, rather, by the distance) they make it back to your shooting subject. A very high-quality black velvet is even deader, provided that the surface fibres are properly aligned for your purposes (the sides of the fuzzy bits are merely black fabric; it's the canyons between the fibres that does most of the actual hard work). That's good and all, but it's not going to get you to the dead black you want to prevent, say, dashboard reflections in windshield glass. (Well, it could work, but you'd need to brush the velvet to suit the shot, so it's no good for video on the go or for quick shooting.) For that, you need specialty stuff.

There are two problems with specialty stuff. One is that it's fragile, so if it's anything that is exposed and needs to last, it's going to need relatively frequent replacement. Every material that does what you want relies on structure as much as colour to do what it do, and that structure won't stand up to much cleaning. The other problem is that it tends to be on the expensive side. Not "mortgage your house" expensive, just a whole lot more than most fabrics, at around $10 to $25 US per square foot (130 to 300-ish € per square metre), depending on the material. And there is stuff that is significantly more expensive - and effective - still, but it becomes entirely impractical for anything except the innards of cameras and optical instruments - all of the increased light absorbency will be killed by ordinary dust and moisture in minutes. A couple of possible solutions are Fineshut SP and VL Flocksheet, both by KoPro and available at Amazon. (The company makes black, and that's about it. They're the makers of Mosou Black paint as well.) Fineshut sheets are meant to line optical instruments of various sorts, with the SP version being the high-cost-but-maybe-practical end of what you're looking for, depending on budget. Fineshut KIWAMI is the stupid-expensive stuff you really don't want to waste money on. It's the best stuff out there for other uses, but not for your use case. Flocksheet is more of a TelePrompTer-liner sort of thing, which is more or less what you're looking for. Again, they're all fragile to one degree or another, but that's what makes them work.

Another product mentioned here is Cinefoil. Great stuff, but not at all what you're looking for. Cinefoil's party trick is that it's heat-resistant while being pretty darned black. That means it can be used near hot lights. And being foil, it can easily be shaped. Needless to say, that makes it the ideal thing for impromptu light-shaping tools. It's also great for killing reflections from light stands and so forth, mostly because there's going to be a roll or two or three of the stuff in your gear bag or on your tape-and-gel rack in the studio. When it's the right stuff, it can't be beat, but it's not the right stuff for the case you've laid out. It's matte black, but it's not nearly black enough or matte enough. You want something that looks like somebody pulled a Looney Toons portable hole out of their pocket and threw it on the surface you want to get rid of. Cinefoil isn't that. Optical blacks are.

Well, they mostly are, at least. Light them bright enough and crank the exposure up high enough, and you'll be able to shoot them. If you're parked in full sun at high noon and trying to get shots of something at the back of a dimly-lit parking garage, physics doesn't really care about your feelings... or your job. Slightly less than one percent of an awful lot is going to drown out 80 percent of next to nothing. You'd need to make sure that the light doesn't make it to your side of the glass in that case (with shades), to the extent that you can. Black materials can only do so much.