No. It is exactly what it is written as. "If you were at the beach, you would have seen the shark." It's not saying you were there or not, it's saying that you probably should maintain knowledge of the following clause. I suppose it could also mean you were not there. But not always.
I can see why they'd get upset if I was assuming they're not Korean. But that's not what I said or meant.
It would be considered directly saying that if I were to say "You can't be Korean because ____" or "You would be Korean if you ______".
It may not be what you meant, but it is what you inadvertently said.
I think you might be thinking of a similar construct which doesn't imply it's false: "If you're Korean, you realise ...". The "you" here is non-specific, and the phrase doesn't say you're Korean or not Korean. The present tense and lack of speculative "would" are what make the difference.
"If you were at the beach, you would have seen the shark." is saying you were not at the beach, and implying you didn't see the shark.
"If you were tall, you would have been able to see it" is saying you are not tall, and implying you couldn't see it.
The "if", "were", and "would" make the phrase a hypothetical counterfactual, imagining that the statement is true and supplying a consequence, and this means that the statement is actually false (i.e. you were not at the beach). This meaning holds when speaking about a specific "you", like the person you're replying to. I'm sure there's a name for this grammatical construct, but I don't know it.
The sentence may be incorrect, in which case the person you're speaking to could correct it with "I was at the beach, but I didn't see it", "I saw it by climbing on a rock", or "WTF I am Korean". It's possible the speaker may suspect their sentence is incorrect and be using it to ask a question indirectly, inviting correction.
A more general meaning is possible when you're not talking about a specific person, but using the conditional to imagine a group of people or something, e.g. "If you were employed, you could afford it, and if you were on a benefit you could afford it, so most people can afford it." I think this usage is uncommon though, as there are much clearer ways to phrase that sort of thing. It's definitely not the usage you wrote.
Source: Native English speaker, but not trained grammarian. Also wrote way too much because it's late at night and I can't be succinct.
I can see why they'd get upset if I was assuming they're not Korean. But that's not what I said or meant.
It would be considered directly saying that if I were to say "You can't be Korean because ____" or "You would be Korean if you ______".