Redisはセマンティックバージョニングを採用しているため、メジャーバージョンのアップデート以外は基本的には後方互換性がある。
https://redis.io/topics/releases

Versioning
Stable releases liberally follow the usual major.minor.patch semantic versioning schema. The primary goal is to provide explicit guarantees regarding backward compatibility.

6のリリースノートに後方互換性がない事項について記載があった。
https://raw.githubusercontent.com/antirez/redis/6.0/00-RELEASENOTES

Migrating from 5.0 to 6.0

Redis 6.0 is mostly a strict superset of 5.0, you should not have any problem
upgrading your application from 5.0 to 6.0. However this is a list of small
non-backward compatible changes introduced in the 6.0 release:

• The SPOP <count> command no longer returns null when the set key does not
  exist. Now it returns the empty set as it should and as happens when it is
  called with a 0 argument. This is technically a fix, however it changes the
  old behavior.

SPOPコマンドを使用していなければ、基本的には問題ないだろう。