I’m not asexual, but I can imagine how it must feel to be dismissed in the ways you describe. It would be nice if people weren’t so defensive, because nobody chooses their sexuality and nobody lives in a vacuum.
As for your first question, it certainly is possible to want, and even have, an intimate romantic relationship without sex. But it is, sadly, difficult to find other people who don’t place a high (even overinflated) value on sex, over friendship - which is what good relationships are based on.