It is the very old GPU / drivers, not the API style it self.
This is something that comes up a couple of times a year.
I'd caution you to be absolutely certain that the hardware you're targetting is still actually in use before imposing this limitation on yourself. Have you researched your target audience or are you working from gut feeling/personal preference here? Because nowadays "very old hardware" can have multiple meanings and they may be surprising.
First of all there's the really really old first-generation consumer-level OpenGL accelerators, dating to 1996/1997, and you almost certainly don't want to target these. These support OpenGL 1.0 with extensions, best case OpenGL 1.1, have limited support for blend modes, may not even support the old lighting models, typically use a minidriver which only implements a subset of OpenGL anyway, and the drivers are just not going to work on any modern (or even 10-year-old) OS.
Secondly there's the first batch of actually good hardware from the likes of NVIDIA or ATI, dating to 1999 or thereabouts. Typically OpenGL 1.3 to 1.5 with a fully-featured driver, but once again having a driver that actually works on an OS that the typical end-user has may be difficult.
Thirdly there's the first generation of shader-capable hardware worth taking seriously, dating from 2004/2005 or so. OpenGL 2.0 but you'll find some weirdness or limitations (for example non-power-of-two textures dropping to software emulation).
The third class of "very old hardware" is the one I'd make a case for being your minimum baseline. It's 10-year-old hardware, you're realistically just not going to encounter anything older in the wild, outside of specialist/enthusiast audiences, so it's perfectly reasonable to say "below this level I will not go".