Settle down, everyone. Let's all take a few deep breaths!
Let's be mature when we have this kind of discussion, yes? Everyone please be aware of the fact that different labels have different connotations for everyone, and are highly highly dependent upon the social context in which they are used.
The important thing to take away from this thread is that if you feel a certain label doesn't, or should not apply to you (because you perceive it to have certain negative connotations), then it is on you, the recipient of that language, to decide how you respond to it. In most respectful social situations, simply telling someone "please don't call me that, I don't appreciate it and find it offensive" is going to be enough to get someone off your case.
The other situations are when you have to decide whether you care enough about altering this person's opinion to get into the discussion with them. Online YouTube/Reddit/Social Media troll? Fuck them, they're not worth your time and are probably just trying to get a rise out of you because they get a kick out of it. Idiots on the street who are judging you based on the way you present yourself? Fuck them too, they don't know shit about you. Their opinion of you is irrelevant, and haters gonna hate.
If it's anyone whose opinion you actually care about that is using this language towards you, go through it with them and maturely, civilly try to understand whether they feel it's socially appropriate to use that term, and if so, WHY they feel it's appropriate, while at the same time communicating why you feel it's not appropriate. You might convince them, or who knows? They might convince you.
Keep in mind that some people are just going to believe what they believe.
To deposit my civil opinion into this thread, I don't find the phrase "otaku" to be demeaning or derogatory at all. To me, it's the connoisseur equivalent for someone who enjoys a lot of anime. The same way you call someone who enjoys a lot of great food you might call a "foodie."
The term "weeaboo," on the other hand, I agree has negative connotations. I see it used to demean, to inflame, to put down someone for their hobby or for the thing they have interest in. To me, "weeaboo" is similar to calling someone who enjoys a lot of great food a "fatty" or "fatass" or similar phrase (regardless of their actual weight/appearance).
If your desire is to avoid or to free yourself from these labels, then it's on you to either educate the people who use them against you, or to demonstrate on your own that the connotations associated with this label do not apply to you.