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I struggled with the C chord for months and still do occasionally. The secret for me was to do dedicated, isolated practice for 5 mins every day for 3+ weeks.
My steps were
– position my fingers and pick each string, if I had a muted string then slightly reposition the offending finger and repeat the above until every string rang clearly.
– keeping my hand positioned I would then press down hard on the strings and then release the pressure, but keep contact with the string. Repeat this 20 times
– I would then lift the fingers off the strings and 1/4” and repeat step 1.
– once I was consistent with that I would take my hand off, put it on my knee then back to the C chord shape and repeat step 1.
I sucked at this for the first few weeks, and then suddenly my fingers were going to the right position.
I know this isn’t exactly the issue you were asking about, but the step 1 is the key. Slowly move and reposition your fingers until you aren’t muting any strings.