Asexual?!?

If I'm Asexual, can I be in a relationship with someone who is straight? I just saw a post about a girl asking about how she is dating a man who is asexual and she had questions about the sexuality.. and almost all the comments said something like.. "RUN... if he is asexual, Run! Because it will only cause problems in the relationship"

But... Just because I'm Asexual and I'm not sexually attracted to another, doesn't mean I'm not allowed to have a romantic relationship?? Is this really how people think? If I were to tell my boyfriend today that I was asexual, will he run too? Will he leave because of it? Am I, or any asexual, not allowed to feel loved or in a happy relationship.. just because I don't crave for sex like most people?

I really need some opinions guys..