Try
Replace[{1, 2, 3, a, b, c}, {i_Integer -> i*2, s_ -> x}, {1}]
which gives me
{2,4,6,x,x,x}
That did the trick. Thank you!
Hmm, that doesn't work, I'm afraid.
{1, 2, 3, a, b, c} /. {i_Integer -> i*2, s_Symbol /; Head[s] != List -> x}