When implementing a differential protection for a transformer is there a problem if the accuracy class for the transformer primary CT is class C400 and the secondary CT at the switchgear is C200?
That depends entirely on the fault current levels and X/R ratios of the system the CT's are connected to. One potential issue is if only one set of the CT's saturates for a through-fault and the relay calculates a differential current above the pickup threshold, then you have a risk of nuisance trips.
In modern relays you can adjust the differential characteristic slope settings to help account for this, at the cost of raising lowering the sensitivity of the element. The calculations are relay specific and depend on how each relay manufacturer calculates the restraint current.