Interesting connection?

In "Lighthouse", Jack tells David that he connected the cable in his room so he could watch the Red Sox, making it seem that David is, like Jack, a Red Sox fan. However, the photo booth pictures of the two of them had David wearing, very prominently, an LA Dodgers hat. Was this meant to show the disconnect between Jack and David, or is it another of the little inconsistencies in the new timeline?

Or, could it be I'm just looking way too hard into a baseball connection?

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