CD-HIT will remove all sequences that share identity above a certain threshold. If you set that threshold at 1.0 (meaning 100% identity), it will remove all identical sequences and retain only one representative:

cd-hit -i my_file.fasta -o my_file_nonredundant.fasta -c 1.0

seqkit common finds common sequences of multiple files by id/name/sequence

seqkit common --by-seq  --ignore-case  --only-positive-strand \
    --infile-list <(find dir/ -name "*.fasta" ) -o common.fa

seqkit grep can exlude a list of records via ID/name/sequence/sequence, common sequences here.

# common sequences, one record per line
seqkit seq --seq --line-width 0 common.fa -o common.fa.txt

# output dir
mkdir -p uniq

for f in dir/*; do
    b=$(basename $f);
    seqkit grep --by-seq --only-positive-strand --invert-match \
        --pattern-file common.fa.txt $f -o uniq/$b
done

The method above compares sequence by the whole bases/amino acids (exact match), you may also use clustering methods, which might be more reasonable for proteins.