For example:
We're currently overbooked at the moment.
For example:
We're currently overbooked at the moment.
Yes, it is redundant since "currently" and "at the moment" mean the same thing. Instead, you could say either:
We're currently overbooked.
or
We're overbooked at the moment.
"Currently at the moment" (as a lot of people say)is redundant and a typical example where it has become fashionable to use "currently" and people add it regardless. These things usually disappear when the word (e.g. 'currently') goes out of fashion. Permanent fixtures also exist: It's raining outside...
We're currently overbooked at the moment.
In this construction the words "currently" and "at the moment" both approximate to "now" and indeed one of the modifiers is redundant.
However, consider
Hotel Manager: "How are the bookings going?"
Receptionist: "At the moment, we're currently overbooked but I am expecting cancellations because of the rail strike."
Here, it is not so clear that there is redundancy. "At the moment" = "at the time of your asking"; "currently overbooked" is a known state and familiar phrase but will be temporary.
This construction is not objectionable.
You should also take note of the comment by tchrist in another post:
Many questions along the lines of "Is XXX YYY redundant?" assume that redundancy is somehow a bad thing or a superfluous thing or a sloppy thing. They presuppose that a "yes" answer would somehow mean something is "wrong" that needs to be "corrected" by one or another piece being removed. As this answer observes, “So though it's redundant, it does not mean it's not a useful and acceptable way to express an idea more clearly.” See the Wikipedia article about all this.
It's redundant routinely to use 'currently' with the present tense, just as it's wrong to use 'previously' with the past tense. 'We are overbooked' and 'We are currently overbooked' mean the same, just as 'we were previously overbooked' and 'we were overbooked' mean the same. The only point in using the adverb is to emphasise something temporary e.g. 'We are currently overbooked but we expect that to change shortly.'
Beware redundancy in language. There is no difference in meaning between 'Please keep all your belongings with you' and 'Please keep your belongings with you'. You can spot redundant words by posing the question 'As opposed to...?' 'Please keep all your belongings with you' as opposed to 'Please keep some of your belongings with you'?