I think, like most others have said, the truth is that some men will mind and some will not. And that's ok. Sometimes you just have to work with the world as is, not how we wish it would be.
I would say that according to some people on this thread I am pretty "shallow" and "superficial." In so far as physical attraction is important to me in a relationship and, yes, that attraction is based to some extent on looks.
Having said that I have been wildly attracted to a man who was very overweight. Normally I would have considered that degree of obesity to be a deal breaker, but this guy was so sexy to me - the way he moved, the way he was socially, his flirtatious confidence... my god. I just wanted to pounce on him. So there you go. By the same token I have known very conventionally handsome men who just haven't done anything for me.
My conclusion is: there is a difference between beauty and attractiveness. Very few people are conventionally beautiful. Work on being attractive. That comes from humour, carrying yourself with a degree of ease and confidence, being interesting, and making the most of the looks you have.