But, if CM-D conversion occurs within the amp's well-behaved range (say, below GBW), and you filter that down later to the desired signal BW (assuming it's lower), you cut out the CMRR and avoid spooky effects (rectification, etc.).
If you need high BW and can't afford excess GBW, you have more limited options.
Worth noting most precision amps claim EMI immunity, though they never go into detail what that constitutes, or how effective it is. As far as I know, it's usually an RC filter at the input pin, so there is some impact on e_n and Cin, and some opportunity for imbalance anyway; but again, who knows.
Tim