One solution is to not volunteer the fact that you train, or get into discussions about it unless someone seems sincerely interested. Think of it like stamp-collecting: why would they care? It's not their thing, so why would you expect them to understand it, or why it matters to you? I don't think that hardcore stamp-collectors get upset because 99.999% of the people they encounter don't get stamp-collecting. They don't "have to face these misperceptions all the time", and neither do we, as long as we keep it to ourselves.
with all due respect, I don't think I agree with this statement. O'Sensei wasn't just a great martial artist; he was an apologist or missionary to some respect in the power of Budo and his Aikido in particular to help bring peace to the world. Now Aikido isn't a religion but it does have similar values and goals. To develop character, morality, temperance, forgiveness and peace. Budo is a lifestyle. Aikido therefore sees itself as a positive force or influence within the world. If someone chooses to make Aikido their 'hobby' or integrate it into their lifestyle, even allowing it to redefine their lifestyle then they believe it has worth. Why omit or deny such a positive influence Especially if you are passionate and ethusiastic, it is incredibly hard to conceal as it becomes a part of you.
Anecdotally, I got talking about my Aiki-Jujutsu on a school trip once with a colleague and he told me that he had seen a marked increase in my confidence at work and the way in which I carry myself around the school. I was totally unconscious of any such signals I was transmitting. I don't go around flaunting I am a martial artist or reminding people I train twice a week, but people find out, it comes up in conversations and yes it means dealing occassionally with misconceptions but it is definitely not something I hide for fear or impatience of having to deal with people's ignorance.