Upon activation of The SegWit Omnibus Changeset, previously fully-validating nodes are rendered non-validating nodes, as they are incapable of validating SegWit transactions.
Upon activation of the Classic hardfork, around 25% of nodes on the network--probably more since the activation threshold only counts miners and plenty of people seem fond of running old node versions--would be either forced to upgrade or kicked off the network entirely... unless the user ecosystem (vendors, exchanges, etc...) isn't supporting Classic anyways so 75% of miners just end up forking themselves onto something no one uses
Yes, segwit activation will cause non-upgraded nodes to lose some functionality in that they will be unable to participate in new segwit transactions, but this is so obviously better than the alternative of a hardfork which would just kick them off the network entirely.