Python 3, 169 101 93 91 85 bytes

lambda s,j="".join:j(chr(int(j(str(int(b<"C"))for b in c[::4]),2))for c in s.split())

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Explanation:

lambda s,j="".join:  # Create a lambda function
    j(  # call "".join, adds characters together with nothing in between
        chr(  # character by int
            int(  # string to int
                j(  # "".join again
                    str(int(b<"C"))  # 1 or 0, based on what character we get
                    for b in c[::4]  # For every first of 4 characters
                ),
                2)  # Base 2
        )
        for c in s.split()  # for every group of Fizz and Buzz with any whitespace character after it
    )

Python 3, 169 101 93 91 85 81 bytes

lambda s,j="".join:j(chr(int(j('01'[b<"C"])for b in c[::4]),2))for c in s.split())

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Explanation:

lambda s,j="".join:  # Create a lambda function
    j(  # call "".join, adds characters together with nothing in between
        chr(  # character by int
            int(  # string to int
                j(  # "".join again
                    '01'[b<"C"]  # 1 or 0, based on what character we get
                    for b in c[::4]  # For every first of 4 characters
                ),
                2)  # Base 2
        )
        for c in s.split()  # for every group of Fizz and Buzz with any whitespace character after it
    )

Python 3, 169 101 93 91 bytes

print("".join(chr(int("".join(str(int(b<"C"))for b in c[::4]),2))for c in input().split()))

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Explanation:

print(
    "".join(  # Join all strings with nothing between them
        chr(  # get character by int
            int("".join(  # turn string of numbers into int
                str(int(b<"C"))  # Get 1 or 0, depending on the character
                for b in c[::4]),  # Do the above for every first of 4 characters
            2)  # Base 2
        )
        for c in input.split()  # Do the above for every chunk of Fizz and Buzz ended by a whitespace character
    )
)

Python 3, 169 101 93 91 85 bytes

lambda s,j="".join:j(chr(int(j(str(int(b<"C"))for b in c[::4]),2))for c in s.split())

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Explanation:

lambda s,j="".join:  # Create a lambda function
    j(  # call "".join, adds characters together with nothing in between
        chr(  # character by int
            int(  # string to int
                j(  # "".join again
                    str(int(b<"C"))  # 1 or 0, based on what character we get
                    for b in c[::4]  # For every first of 4 characters
                ),
                2)  # Base 2
        )
        for c in s.split()  # for every group of Fizz and Buzz with any whitespace character after it
    )

Python 3, 169 101 93 bytes

print("".join([chr(int("".join(str(int(b<"C"))for b in c[::4]),2))for c in input().split()]))

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Python 3, 169 101 93 91 bytes

print("".join(chr(int("".join(str(int(b<"C"))for b in c[::4]),2))for c in input().split()))

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Explanation:

print(
    "".join(  # Join all strings with nothing between them
        chr(  # get character by int
            int("".join(  # turn string of numbers into int
                str(int(b<"C"))  # Get 1 or 0, depending on the character
                for b in c[::4]),  # Do the above for every first of 4 characters
            2)  # Base 2
        )
        for c in input.split()  # Do the above for every chunk of Fizz and Buzz ended by a whitespace character
    )
)