If I have original Casascius coins, will it be possible to redeem them years from now
Yes. As long as Bitcoin continues to exist and have value, it would be possible to redeem them.
or will the private address at some point become incompatible with the blockchain?
No. That's not how bitcoin works. It cannot become incompatible with the blockchain.
In case you weren't aware...
That Casascius coin has BOTH
Bitcoin value AND
Bitcoin Cash value. It can be redeemed for either or both.
(Assuming that the Casascius coin hasn't been compromised and had its private key leaked/stolen.)