cmoy with 1uF input cap, DC offset from source still getting through

[morfic]

So it's not actually needed, does it affect my DC offset?

[Conrad Hoffman]

Never say never but no modern opamp I've tested has been much affected by asymmetric supplies, including offset. What you see at the output is controlled by the feedback values and bias currents. And maybe the signal

If only one supply is available you can create a resistive divider ground and buffer it- the "rail splitter" ICs, but a real ground between two supplies is far better from an impedance and stability POV.