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Is the comma in the following sentence unnecessary or does it help emphasize the second phrase within the sentence?
“The stories were insightful, and so relevant to today's political discussions about the value of immigrants to our country.”

i don’t really know for sure, but I personally think that it’s kinda unnecessary. If you have it there it’s good but if you remove it - it's still is good.

As far as I know, there's only supposed to be a comma before "and" if an independent clause follows. So if the sentence said "and they were so relevant..." you would have to put a comma before "and." As the sentence is, the comma isn't necessary.

I don't think the comma is necessary. It does not emphasize the second clause in the sentence. It brings a slight pause in the sentence and breaks the continuity. Also, as maggi3 mentioned, "," before a co-ordinate conjunction such as "and" should be used when one is connecting 2 independent clauses. An independent clause has a subject and a verb of its own.

The comma is incorrect as there is an independent clause connecting a dependent clause.

As others have said, the comma is incorrect, but here's why it's tempting. In speech, many people would pause before the second adjective in order to add emphasis: "insightful [small pause] and so relevant to..." In text, commas are one standard way to indicate a pause. In order to keep the pause, one could repeat the subject: "insightful, and they are so relevant to..."

I also want to add that there's another way to read this sentence. The words "and so" could be understood as the beginning of a result clause. If that were the case, the correct construction would be: "insightful, and so [they are] relevant to...", but a native speaker might drop the bracketed words, producing a perfectly intelligible but grammatically incorrect construction. The result clause would imply that they are relevant because they are insightful, rather than simply stating that they are both insightful and relevant. In speech, I would be able to differentiate between the conjunctive and adverbial uses of "so" by the speaker's tone. In text, one would need to add a second comma: "insightful, and so, relevant to..." But honestly, if I wanted to indicate that relationship between the modifiers without a full result clause, I'd use a clearer indicator such as "therefore," and then I'd skip the comma: "insightful and therefore relevant to..."