I am new around here (just joined today) and I only want to say that I struggle with C and F both, so I think we are both normal. Sounds like these finger positions are challenging for us who are just starting out. It was actually my attempts to find good practice tips, techniques and ideas for these two challenging chords that led me here. So thank you for asking this great question and letting me eavesdrop on the great advice in here!
I am slowly getting better at playing it without muting and am able to hear each note, now I just need to learn how to transition in and out of the chord. Slow and steady wins the race.