String action is too high?
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Changing strings or tuning isn't going to do much. The problem is the extra height causes the tension for the length to be too much. What may help is to lower the nut [or deepen the notch a bit], make sure the string is touching the bridge as far back as possible and kind of split the difference between sharp/flat [open/affected fret]. It should be ok to be on the slightly sharp side rather than the flat side as flat is annoying and more obvious. If it's less than about 10 cents [usually in the green on the tuner] it is probably acceptable to most folks.