"Ultimately, as always, we compromise and her tea is a pale brown". Isn't the "a" redundant here? It sounds wrong to me.
The sentence is fine with or without the "a". And the meaning is basically the same in both cases, even though grammatically it's different.
"Her tea is pale brown" - here, "pale brown" is an adjective.
"Her tea is a pale brown" - "brown" is a noun (i.e., 'a brown color'), and "pale" is an adjective modifying it.
No, it's not wrong. When a color term modified by an adjective (like "bright red"; see the previous question "Bright" Part of speech) is used as a predicate, it's idiomatic to put the indefinite article in front. The use of the indefinite article is not mandatory, though (it would not be incorrect to say "Her tea is pale brown"). As Mike Baranczak mentioned, color terms like "brown" are used both as nouns and as adjectives.
If the word "pale" were not in the sentence, it would sound unnatural to use "a": we wouldn't say "her tea is a brown". But we could say "her tea is a muddy brown" or "her tea is a deep brown".