I have heard the word 付き合う used to mean "interact with/hang out with" but I have heard it more often to mean steadily dating someone. How can you tell the meaning from context and how could you say that you interact with someone in a way that's clear you're not dating them?
In general Japanese usage (in most everyday situations), 付き合います used with a person that is not outright understood to be a relative or superior from a statement meant for a third party-listener most likely almost immediately implies some form of romantic relationship with the said person.
to you: サラさんと付き合ってます。 I'm going out with Sara. (Unless you know that to the speaker, Sara is a relative or a mere colleage.)
to you: 客先にサラさんに付き合います。 I'm going to the client's place with Sara. (It's explicitly mentioned a work affair.)
to you: 病院まで付き合いますよ。 I'll go with you until the hospital.
In the first place, the speaker will unlikely make such statement unless there is some level of familiarity with the listener.
This should help.
I think the context is drawn from other components of the sentence. Think how in English it is possible to say "I'm seeing Sara" and "I'm seeing Sara at the park in 20 minutes" and also "I'm seeing Sara over there all by herself" and suddenly "seeing Sara" means three different things.
The thing you want to focus on is the emphasis and word choice for the sentence that accompanies 付き合う as 付き合う definitely means "to get together, hang out, interact" but in a specific context and word choice the implication is that you're "getting together, hanging out, interacting" (exclusively) with a specific person. Consider the following:
I'm getting together with my friends in front of the movie theater.
Right now I'm not dating anybody.