Here's a version that uses a HoH to allow multiple changes to multiple contexts in one pass.

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1227916

use strict;
use warnings;
$SIG{__WARN__} = sub {die @_};

##################### configuration section

my %changes =
  (
  ObjectType1 => { Param1 => 0, Param2 => 'SomeOtherText' },
  ObjectType4 => { Param3 => 'Replacement' },
  Foo => { Param2 => 'FooChanged' },
  );

##################### end configuration section

my $allcontexts = join '|', sort keys %changes;
my $contextpattern = qr/\b($allcontexts)\b/;
my %patterns;
for my $section (keys %changes)
  {
  my $all = join '|', keys %{ $changes{$section} };
  $patterns{$section} =qr/\b($all)\b/;
  }
local $/ = "\n}\n";
while( <DATA> )
  {
  if( /$contextpattern/ )
    {
    my @context;
    print $& while
      @context && $patterns{$context[-1]} &&
        /\G(\h*$patterns{$context[-1]} = ).*\n/gc ?
        "$1$changes{$context[-1]}{$2}\n" =~ /.*/s :
      @context && /\G\h*\}\n/gc ? pop @context :
      /\G\h*([\w ]+)\n\h*\{\n/gc ? push @context, $1 :
      /\G.*\n/gc;
    }
  else
    {
    print;
    }
  }

__DATA__
ObjectType1
{
   Param1 = 8
   NestedObject
   {
      Param1 = 3
      Param2 = SomeText
   }
   Param2 = SomeText
}
ObjectType2
{
   Foo
   {
      Param1 = StaySame
      Param2 = FooChange
      ObjectType4
      {
         Param1 = DoNotReplaceThis
         Param3 = ReplaceThis
      }
   }
}
ObjectType1
{
   Param1 = ReplaceThis
   Param3 = DoNotReplaceThis
   Foo
   {
      Param1 = StaySame
      ObjectType4
      {
         Param1 = DoNotReplaceThis
         Param3 = ReplaceThis
      }
   }
}
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