Graphics, as in graphical fidelity, polygon count, etc. are valueless to me.
Art style is everything. I don't care if I can see the pixels in the game, I still play the same SNES my family had 25 years ago. The game has to look good, and graphical fidelity is a tool to help achieve that, but it's only a tool, and useless without the appropriate art direction.
The overall look and feel of a game certainly have turned me away many times, but graphics in the technical term of having low res textures or simple lighting not really, other than ones with performance issues.
I might be the exception, but personally, graphics mean nothing to me.
I've had as much fun with 8-bit games as I have with modern ones. I'm always amazed with how much better the games look, but that won't keep me playing of it's just not fun.
Of course the exception would be graphics that are so bad that they get in the way of playing, or I'm unable to tell what things are supposed to be.
Yeah I definitely might not be as drawn to a game with graphics not to today's standards, but if the core mechanics are good I quickly start to ignore the graphics.