I've certainly never tested it with conditionals.

I think it's the conditional indeed, because it works smoothly when I re-write it to not use a conditional:

%
    ^
    \s*
    (                               # <1>
        # Single tags like <foo/>
        <
        \s*
        [a-zA-Z:]+
        (?:
            \s*[a-zA-Z:]*
            \s* = \s*
            (?:'[^']*'|"[^"]*")
        )*
        \s*
        /\s*
        >
    |
        # Tags in pairs like <foo>content</foo>
        <
        \s*
        ([a-zA-Z:]+)                # <2/>
        (?:
            \s*[a-zA-Z:]*
            \s* = \s*
            (?:'[^']*'|"[^"]*")
        )*
        \s*
        >

        (?:[^<>]* | (?1))*

        <\s*/\s*\2\s*>
    )                               # </1>
    \s*
    $
%x
[download]

<foo><bar></bar></foo> # Match
<foo><bar></foo></bar> # No match
<foo><bar/></foo>      # Match
<foo><bar></foo>       # No match
<foo bar=baz/>         # No match
<foo bar="baz">        # No match
<foo bar="baz"/>       # Match
< fooo   /  >          # Match
<foo/>foo              # No match
foo<foo/>              # No match
<foo>foo</foo>         # Match
<foo><bar/>foo</foo>   # Match
#<a><b><c></c></b></a> # No match (WRONG!!)
[download]

Now, there's still the three-level-deep problem...

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W5kIHBhY2soKS4gQnV0IGRvIHlvdS
ByZWNvZ25pc2UgQmFzZTY0IHdoZW4
geW91IHNlZSBpdD8gIC0tIEp1ZXJk