Oooh! What a minefield!
I think this is very complicated, perhaps without a definitive answer.
Personally, I'd use either. The first agrees with sentences in the subjunctive such as, "It's essential he BE here tomorrow." So that's a point for using SEE. However, many people, especially in the UK, would use IS rather than the subjunctive. As you know. (It's essential he IS here tomorrow.) So that's a point for using SEES!
If I'm feeling formal I'll go for the subjunctive: SEE.
If I'm chatting to a friend: SEES
It won't be a conscious decision. It'll just come out of my mouth. My BRAIN will be aware of the subjunctive nature and that's why SEE might come out.
We have more questions here!
Is the subjunctive dying? I'd say, yes! But I like it!
Does the use of NO ONE confuse the issue? People sometimes argue if NO ONE is singular or plural. I just mention this as a possible source of muddle.
Does PREFER work in the subjunctive in other sentences? Let's try it:
I prefer that Harry BE/IS here.
It is important (that) Harry BE/IS here. Clearly BOTH correct in this one! But I suspect Americans would prefer the BE/subjunctive.
What do you feel?
My feeling is that PREFER is a wee bit borderline. Whilst I like, "I prefer that no one SEE me like this," I do NOT particularly like, "I prefer that Harry BE here." Or do I? If I say it a few times, like the Queen of England, very poshly, I start to like it!
I really need to explore this more. I suspect Shakespeare would have something to say about this.