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In English, we say "you" when referring to a hypothetical person (for example, "the shop allows you to pay without cash" where you refers to people in general). Would it be the same in Spanish or can you use third person?
For example:
La libertad de expresión es el derecho de decir lo que quieres decir sin censura.
or
La libertad de expresión es el derecho de decir lo que quiere decir sin censura.
Although the other answers are essentially correct, I think there are a couple of details left.
Your two sentences are grammatically correct:
Number 1 has an implied tú, that is, the second person singular personal pronoun, which is informal. This sentence works as a general statement exactly in the same way as it would in English with you.
But number 2 has a small problem: the verb appears in the third person singular, but the implied pronoun could be a third person singular one (él, ella) or the formal second person singular usted. (The fact that usted takes a 3rd person verb doesn't make it less of a 2nd person pronoun.) If you're talking to someone that you would address as usted, the sentence will probably be understood as a general statement, as with number 1. But if not (if you're talking to a close friend, for example), it will sound like you're referring to some (unknown) third person (some él or ella), and therefore it will be confusing.
So sentence number 2 should probably use usted explicitly if you're trying to be formal:
La libertad de expresión es el derecho de decir lo que usted quiere decir sin censura.
There are two more common and less awkward ways to express this kind of general statement. One is using the pronoun uno (like English one), with the verb in the third person singular as in sentence number 2.
La libertad de expresión es el derecho de decir lo que uno quiere decir sin censura.
The other is using an impersonal construction with the pronoun se:
La libertad de expresión es el derecho de decir lo que se quiere decir sin censura.
Although it looks like a simple substitution, using the "impersonal se" is a bit more complicated, so I'll leave it at that, only mentioning it for the sake of completion.
Both of these solutions (with uno and with the "impersonal se") are neutral with respect to the hearer, i.e. you can use them equally correctly with people that you address as tú or with those that you address as usted.
They are both correct. Which one is the best, that will depend on the context. If you are writing a text in a book or article, or if you are writing a more formal text, or yet- if you are writing to people you may not know - you might want to stick to the 3rd person (usted). If you are writing to friends, to people you know and have a relationship with or in a less formal context such as social media - you might want to stick with 2nd person (tú).
In English it's pretty much the same, right? Using your example - you might say as well "the shop allows one to pay without cash" - and that would be an example of using 3rd person instead of 2nd person in English...
They are both correct. The first one, in particular, could refer to you and any other people; the second choice is formal and educated, and you could use it with older people.
