A, Buzz, C, D, E, Fizz, G

Python 3, 180 174 168 160 152 bytes

from sys import*
J=''.join
L=str.lower
s,a,b=J(stdin).split(', ')
print(J('FBFBiuIUzzZZzzZZ'[L(k)==L(b)::2][k!=L(k)::2]*(L(k)in L(a+b))or k for k in s))

This is just a more golfed version of Stephen's answer, in Python 3. This chips away 42% of his bytes. Python 2 would save one byte on the print, but such is the price of progress. This handles newlines properly.

Thanks to Blckknight for saving 8 bytes on input.

Python, 109 bytes

lambda s,w:"".join([c,"Fizz","Buzz","BUZZ","FIZZ"][-~w.lower().find(c.lower())*-~(-2*c.isupper())]for c in s)

Try it online!

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Takes the two characters as a single string

Edit: Added testcase to TIO link, newline works too

Jelly, 34 bytes

Œl=€⁹Œl¤ȧ€"“¡Ṭ4“Ụp»o"/ȯ"Œu⁹Œln$T¤¦

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How?

Œl=€⁹Œl¤ȧ€"“¡Ṭ4“Ụp»o"/ȯ"Œu⁹Œln$T¤¦ - Main link: characters, string
Œl                                 - lowercase the characters
       ¤                           - nilad followed by link(s) as a nilad:
    ⁹                              -     right argument, the string
     Œl                            -     lowercase
  =€                               - equals (vectorises) for €ach (a list of 2 lists that identify the indexes of the string matching the characters regardless of case)
           “¡Ṭ4“Ụp»                - dictionary strings ["Fizz", "Buzz"]
          "                        - zip with
        ȧ€                         -     logical and (non-vectorising) for €ach (replace the 1s with the words)
                     /             - reduce with:
                    "              -     zip with:
                   o               -         logical or (vectorises) (make one list of zeros and the words)
                                   - implicit right argument, string
                       "           - zip with:
                      ȯ            -     logical or (non-vectorising) (replace the zeros with the original characters from the string)
                                 ¦ - apply...
                        Œu         -     uppercase
                                   - ...to the indexes (the words at indexes):
                                ¤  -     nilad followed by link(s) as a nilad:
                          ⁹        -         right argument, the string
                              $    -         last two links as a monad (i.e. the string on both sides):
                           Œl      -             lowercase
                             n     -             not equals (vectorises)
                               T   -         truthy indexes (the indexes of the capital letters in the string)