The solution becomes clear when one realizes that qr// regexes are nothing but strings (albiet special string), and that they are not interpolated until runtime. Consider:

    my $inlinetag = do {
        my $acc =
        qr/(?> \{          (?: (?> \\. | [^\\{}]+ | (??{ $acc }) ) )* 
+  \} )/x;
        qr/    \{ (\w+): ( (?: (?> \\. | [^\\{}]+ | (??{ $acc }) ) )* 
+) \}  /x;
    };
[download]

In this modified snippet, the $acc regex is constructed, and scoped lexically to the do block. Next, the unnamed regex is constructed. Note that both of these pass strict checking since $acc was created in the same block, and thus exists. Since the second regex was the last statement in the do block, it is returned, and is assigned to $inlinetag. I believe this is the behavior you expected.

So what is the problem? The problem is that when $inlinetag is expanded at runtime, $acc no longer exists since it went out of scope when the do block returned the unnamed regex and assigned it to $inlinetag. A potential solution is just to get rid of the do block:

    my $acc =
        qr/(?> \{          (?: (?> \\. | [^\\{}]+ | (??{ $acc }) ) )* 
+  \} )/x;
    my $inlinetag =
        qr/    \{ (\w+): ( (?: (?> \\. | [^\\{}]+ | (??{ $acc }) ) )* 
+) \}  /x;
[download]

Or, if you're really worried about cluttering your namespace, you can do some closure magic:

    my $inlinetag = sub {
        my $acc =
        qr/(?> \{          (?: (?> \\. | [^\\{}]+ | (??{ $acc }) ) )* 
+  \} )/x;
        qr/    \{ (\w+): ( (?: (?> \\. | [^\\{}]+ | (??{ $acc }) ) )* 
+) \}  /x;
    };
[download]

However, you must now use it like this: qr/(??{$inlinetag->()}/ rather than like qr/$inlinetag/ with the first method.