The widely used word "homophobia" clearly doesn't fit the criteria. For example, "racism" can mean discrimination towards any race, black, white, Asian, etc. Similarly, the word we are looking for should also be able to describe people who have prejudice towards asexuals, bisexuals, heterosexuals, pansexuals, etc.
Also, phobia means fear, or negative feelings. If someone assumes a black man is a fast runner, loves water melon, and is a great dancer before they have even met him or heard anything about him, simply because he is black, I would argue that that is racist. But those are all positive traits, and therefore there need not be any "phobia" involved.
Similarly, if one assumes a gay man speaks in a feminine voice, is very knowledgable about fashion, interior design, etc. and listens to Village People, I would consider that [insert the word we are looking for here]. But there need not be any "phobia" or negative feelings involved, since those traits can all be seen as positive traits.
Repeating the earlier point, the word we are looking for should also describe prejudice against asexual, or even heterosexual people. Asexuality can also be considered a sexual orientation. Clearly, the word "homophobic" can not be used to describe prejudice against asexual or heterosexual people.
Edit: While the linked question is quite similar, this question is wider and more detailed.
Best Answer
Heteronormativity will suit.
Per Oxford Dictionaries Online (ODO):
Per Wikipedia:
A more specific (and more recently-introduced) related term is cisnormativity.
Per Wiktionary, for example: