Is the opposite of "like" "dislike" or "indifference/neutrality & dislike?"

Not liking and disliking are different notions but could be the same depending on the situation. For example. If you said to me: Do you like custard? I would say "I don't like custard" and I may add "but I don't dislike it". In this sense 'not liking' does not imply a dislike. If you asked if I like root canal treatment I would say that "I don't like root canal treatment" and in this case I am definitely expressing dislike!

I think it depends on context - like so many things.

dislike (verb) = to not like

Cambridge

1: opposite = completely different

OR

2: opposite = being in a position on the other side

Cambridge

The two senses of opposite, although connected, are not the same. It is important to distinguish them:

Using sense 1, dislike (even if it include indifference, neutrality or other shades of partiality), being "not like", is completely different from like, so they are opposites.

Using sense 2, dislike is completely different from like but because "not like" includes indifference, neutrality or other shades of partiality it cannot be seen as having a unique quality or position of being "on the other side" of like.

To give another example. In a completely black and white world, black and white=not black are opposite in sense 1, and in sense 2 (there being only two alternatives). But in a world of many colours, black and white are opposite only in sense 1 but not in sense 2.

Dislike is the opposite of like in the sense of being its gradable antonym: the two concepts are at the opposite sides of a spectrum that also contains the intermediate concept of indifference. In the terminology of logic, like and dislike are contraries (but one cannot assume that the word contrary would be understood that way in an everyday conversation). On the other hand, not like (which includes both disliking and indifference) is the opposite of like in the sense of being its complementary antonym. In the terminology of logic, like and not like are contradictories. Both dislike and not like are thus the opposites of like; it's just that they are different kinds of opposites. The differences among different kinds of opposites are presented clearly in the Wikipedia article on the topic.

The matter, however, gets more complicated when pragmatic considerations are added to the semantic ones. Even though not like, as a matter of semantics, includes indifference, we rarely say that we don't like something when we are indifferent to it. Indifference is more usually conveyed by something like 'I don't care' or 'it doesn't matter'. Because of that, one's saying that one doesn't like something is often taken to conversationally implicate that one dislikes it.