Notice that the Korean literally says "Each other liked each other," which reads and sounds pretty silly and suggests that 서로 was probably not meant to be used as a noun. A better sentence would be the following:
서로가 서로를 좋아했다
They (each other) liked each other.
그들이 서로 좋아했다.In the above Korean sentence, 서로 is being used as an adverb and sounds more natural than when it was used as a noun, but the English translation of the sentence confuses things because "each other" is considered a pronoun in English, which is probably why some Koreans feel inclined to write 서로 as 서로를.
They liked each other.
In his book "우리가 정말 알아야 할 우리말 바로 쓰기," the author 이수열 argues that 서로 was only meant to be used as an adverb and says that using it as a noun or pronoun is a distortion of Korean grammar. He makes a good argument and gives several real-world examples of how sentences using 서로 as a noun can be corrected by simply using it as an adverb. Here are some of the examples.
- 한, 일 요트 경기를 벌여 서로 상호간의 친선을 과시했습니다.
* Replace the phrase in red with just 서로 or 상호.
- 우리는 서로가 서로를 위하고 도와야 한다.
* Replace the phrase in red with just 서로.
- 친구와 가족은 이미 상대자를 잘 알고 있으므로, 서로의 관계가 우호적일 뿐 아니라.
* Replace the phrase in red with 관계가 서로.
- 학습 활동을 중심으로 서로의 의견을 주고 받는 것이 좋은 방법이다.
* Replace the phrase in red with 의견을 서로.
Notice that the Korean in Examples 1 and 2 was made more complicated than it needed to be, and that in Examples 3 and 4, the nouns were placed after 서로 instead of before it.
In Korean, there is no need to use 서로 as a noun or pronoun, so why do some Koreans use it as a noun? I think it is because they have been influenced by the English translation "each other," which is a pronoun.
In Korean, the meaning of "each other" is achieved by using the adverb 서로 in combination with a noun that precedes it. Even the English pronoun "each other" is not a normal pronoun because it is dependent on a noun being in the same sentence. For example, you cannot say, "Each other liked." Therefore, I think using 서로 as a noun is unnecessary and is just another example of Korean being polluted by the English language.
By the way, I have written about 서로 before: "How should we use 서로?"