Should an officer be allowed to continue to serve on Active Duty after being relieved from command?

Two separate issues to me. Technical competence is likely not needed to head up and lead the unit. A basic understanding, definitely.
Leadership to counsel and mentor those in his-her unit, absolute requirement.
Also, being previously relieved of command would depend on circumstances. May not have significance in different billet, particularly a purely staff function.

The Military has a way of dealing with that... Performance Review should address his shortcomings.
If he is not capable, he shouldn't be leading anyone.
If it's that bad, he should be denied re-enlistment.
Too many lives depend on leaders doing the right thing...
Why allow him to continue to lead?
Government Issue that is defective should be replaced ;)
my opinion
caveat: I served under two who should not have been commissioned, imo...
One was delusional and would have gotten our entire unit slaughtered if we went into combat (gung ho busted Pathfinder who was certain an air traffic control unit should be Ranger qualified)... the other was fraternizing on and off duty with his E-4 aide.
Both are probably still serving.

It depends upon why the officer was relieved. Having said that, officers have a senior enlisted who should be keeping them on the right path along with a senior officer who should be giving guidance and corrective steps. If an officer or senior enlisted leader fails it's usually because they entered an environment that they weren't qualified to be in but there are always those who always think they know better than everyone else and soon find themselves on a raft in the middle of the pond without a paddle.

I’ve seen top leaders being “fired” because of mistakes of those under them. If eligible, they may have to retire or else be moved somewhere else, not everyone is a leader but remember, if those under the leaders do not do those best, the leaders may pay the price,

They will run an enlisted member out of the service so the same standard should start within the officer corps too. Incompetence, lack of leadership ability or just a dirt bag, officers need to police their ranks instead of just shuffling their undesirables out of sight.

There is no blanket correct answer. Why was the officer relieved is the start point. Was it it for his bad acts? If so then that officer should be released. If it was for other factors then it depends what they are. Was the officer promoted to a position he could not handle, but he was a good staff officer? If so return to staff position and allow him to continue until retirement. We all know his promotion opportunities have ended, but he may still provide a benefit to the service.

There is no blanket correct answer. Why was the officer relieved of command? His personal bad acts, then no, he should be encouraged to retire. Perhaps he was a better staff officer( who was promoted to a job above his ability) who could actually provide benefit to the Service by returning to a Staff position. Is that officer going to go much further, probably not, but no reason to waste his ability by an early release.

No they should not command well my time in the military in the 70s we had so many command his sergeant majors that were alcoholics and they were no good

Unfortunately, it happens all the time just to allow scumbags to make it to retirement. Billets created, etc., just to give them a place to quietly hide until they can squeak out to save face for a commander/unit/whatever.

I've seen plenty of awesome leaders at the platoon and company levels that completely bombed at the higher levels. Especially as they moved farther away from regular interactions with the junior enlisted. They lost that connection with the foundation of their command as the administrative portion of their duties overrode those times to connect.