I see what you mean in the 90 minutes against Brighton. It is eerily similar to when Rangnick started. Manchester United players revert to type under stress.
They seem to start with a game plan and try to play. But once put under pressure, the same players seem to revert back to how it was under Ole. They don’t seem to unlearn and relearn.
At the 45 minute mark, the team is doing the exact same pattern of play as when under Ole.
For clubs that subscribe to a footballing philosophy like Barca or Ajax, play style does not change.
Now for most clubs that aren’t set on a certain style, there may be changes. See the Everton of today and Everton of 6 years ago under previous management, see the difference in styles?
But sometimes there can be no changes. Some DoF are comfortable in allowing the manager to dictate the play style. See Arteta at Arsenal.
Long answer to the question, depends on the club.
Need to be Bayern larh, a little flexible but not too much, they aint gonna hire a Conte, Simeone, Mourinho etc