Is CRC32 birthday attack independent of input?
The purpose of the checksum is to detect a change of the configuration (e.g. change of serial number by constant device type). In the case of the serial number only single bits can change. 


Actually, the birthday problem does not really apply to CRC; CRC doesn't act like a random function.

For your purposes, it acts better than a random function.  CRC-32 has the property that, if a change you make is limited to 4 consecutive bytes, the resulting CRC will always change.

Hence, if the only change in the configuration is a change to a single 4 byte serial number (and everything else is the same), then CRC-32 will always detect the change (and this remains true even if you change more than one bit of the serial number).

Of course, if additional things change within the configuration (e.g. if two serial numbers are changed), then this need not be true.