I'm firmly on the "it's not okay" side of the debate.
Yes, they're "just characters" but it's a character being piloted by a person as a direct way of interacting with the game-world. It's different to a person playing with an RC car because they're not the car - they're still them, and their primary experience of the world is not coming from the car; nor is it a "human-equivalent" object in the same way an avatar is.
In the game our avatar is the primary point through which we experience the game-world, and we're still "people" having social interactions with each other - therefore I feel like social rules still apply. We wave hello/goodbye, we target people that we're having a conversation with so our avatars will look at each other and make eye contact. At least that's my experience with people in my FC. If someone makes an emote towards my avatar, they are at some level making it towards me, the person they are interacting with via our avatars.
So in the same way, if people act towards my avatar in a way that I don't like, it makes me feel uncomfortable. (There was a guy in my FC who would basically insist on hugs every time he met anyone - and never got the hint how many times I refused that I didn't want to do that. Minor example perhaps, but I didn't want to do it and hated getting asked.)
And while it's true that we don't [fight monsters / cast spells / etc.] in real life, using a character in that context seems like a separate thing to me. It's like two things in one - they're a character we use for the experience of interacting with the grand fantasy story and world, and simultaneously they're an avatar representing our presence in the game-world interacting with other people through it. Killing enemies is "character stuff"; talking to other people is "avatar stuff" and my character wouldn't be having that conversation.
By the same logic, if another character in the story does something to my character, that's directed at her. If another player does the same action-via-emote, that feels directed at me, at least to some extent.
It all comes down to respecting others - not just assuming they should be okay with it because you don't see anything wrong with it yourself.
As for the argument that we don't own our characters and the person 'looking' could just as easily remake that character for themselves... why don't they do that, then? Why stare at the character representing another person (who wants them to stop) when in a few minutes they could have an identical or even more-to-their taste character made in the character creator and under their full control?