How to modify a string of symbols based on the positions of $1$'s in a list of Booleans?

Update: A few additional alternatives:

Make list of functions out of exampleInput:

foo = exampleInput /. {0 -> Identity, 1 -> ToUpperCase};

You can use foo with StringReplace or with StringReplacePart in several ways:

StringReplace[string, "x" ~~ a_ :> "x"<> Last[foo = RotateLeft[foo]][a]]

or (using @J.M.'s regular expression pattern):

StringReplace[string, 
  RegularExpression["(?![x])[a-z]"] :> Last[foo = RotateLeft[foo]]["$0"]]

or

Block[{i = 1}, StringReplace[string, "x" ~~ a_ :> "x"<> foo[[i++]][a]]]

or

pos = 1 + StringPosition[string, "x"];

StringReplacePart[string, Construct @@@ Thread[{foo, StringTake[string, pos]}], pos]

or

StringReplacePart[string, MapThread[Compose, {foo, StringTake[string, pos]}], pos]

Original answer:

StringRiffle[MapAt[StringReplace["x" ~~ a_ :> "x" <> ToUpperCase[a]], 
  StringSplit[string, ","], Position[exampleInput, 1]], ","]

"\\xA , \\xB , \\xc , \\xD , \\xe , \\xf , \\xG , \\xh"

Alternatively,

spos = 1 + Pick[StringPosition[string, "x"], exampleInput, 1];

StringReplacePart[string, ToUpperCase[StringTake[string, spos]], spos]

"\\xA , \\xB , \\xc , \\xD , \\xe , \\xf , \\xG , \\xh"

and

ClearAll[stringMapAt]
stringMapAt = StringJoin@MapAt[#, Characters@#2, #3] &;

stringMapAt[ToUpperCase, string, spos[[All, {1}]]]

"\\xA , \\xB , \\xc , \\xD , \\xe , \\xf , \\xG , \\xh"

A variation of the first answer in kglr's post that doesn't deconstruct and reconstruct the list:

Module[{i = 1}, 
  StringReplace[
    string, "x" ~~ a_ :> "x" <> If[exampleInput[[i++]] == 1, ToUpperCase@a, a]
   ]
 ]

"\\xA , \\xB , \\xc , \\xD , \\xe , \\xf , \\xG , \\xh"

Slightly more verbose but not requiring checking with the If statement:

Module[{i = 1}, 
  StringReplace[string, 
    "x" ~~ z_ :>  "x" <> FromCharacterCode[First@ToCharacterCode[z] - 32 exampleInput[[i++]]]
   ]
 ]

Here's how to use a regex with "negative lookahead" in conjunction with Pick[]:

With[{pos = Pick[StringPosition[string, RegularExpression["((?![x])[a-z])"]], 
                 exampleInput, 1]},
     StringReplacePart[string, ToUpperCase[StringTake[string, pos]], pos]]
   "\\xA , \\xB , \\xc , \\xD , \\xe , \\xf , \\xG , \\xh"