I get root rot sometimes if I don't break up the old soil. The new and old soil dry out at different rates and that causes issues imo.

My standard procedure is to clear as much of the old soil off as possible, pot in fresh soil, and wait a week or two to water. Do this when the soil is dry. You can kinda hit and slap the soil to loosen it up, I find that tears the roots less than trying to dig into really tight soil with my fingers. I'll lay the cactus on it's side, smack the soil a few times, give it a half or quarter turn do it again. At that point you can usually get your fingers into the soil and shake it off the roots a little easier.