The three are all ok and natural. Probably, the last - "I like tea but don't like juice" sounds the *most* natural to me if you are only making a general statement or observation. In casual conversation we tend to drop words where possible and here it's "I" (before don't). Keep in mind the three aren't completely interchangeable. If someone offered me a choice of only 'tea or juice', I would choose the one of the first two expressions. While the 3rd would work, it just doesn't sound as natural in this particular context.

The first two are valid expressions. The second sentence, "I like tea but I don't like juice" sounds less formal and more likely the way someone would say it. The third sentence, "I like tea but don't like juice" isn't correct; the personal pronoun is necessary before the verb ("don't like").

If I am talking about what I like to drink generally, I would not say "but" in those three sentences, as "liking juice" doesn't contradict with "liking tea". I like tea. I don't like juice. I like tea, but I don't like tea with milk.

Thank you.

The first two are valid expressions. The second sentence, "I like tea but I don't like juice" sounds less formal and more likely the way someone would say it. The third sentence, "I like tea but don't like juice" isn't correct; the personal pronoun is necessary before the verb ("don't like").