For example:
We're currently overbooked at the moment.
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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...
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'?