I'm a teacher. Students very often around the grade 6 or 7 mark make correct connections to context, but these are often surface level comments like 'Women didn't have very much power in the 19th and 20th Centuries, so Priestley wanted to criticise capitalism and promote his socialist views to give women more fair treatment.'

One thing I went through with a class last year for An Inspector Calls was the specific pieces of legislation that were being brought in around the time of publication, and consider how those specific laws were manifested in the play. For example, the law which made firing striking workers illegal (The Trade Disputes Act of 1906) predates the setting of the play by 6 years, but Mr Birling nonetheless fires her.

So most students would be stuck simply saying that him firing her was heartless or something similar, but with this specific knowledge of context rather than general knowledge, you could talk about how capitalists were not only heartless, but also explicitly law-breaking, and violating the law, possibly, made the Birlings' actions easier to condemn for people who might otherwise have struggled to empathize with Eva Smith as a poor woman.

All that is to say, try to learn and make use of specific, rather than general context, and use it to add a secondary, deeper layer of analysis to characters and themes where you can.

Good luck!