This is a matter of style. Your following The Chicago Manual of Style would produce:
a Haunted Mansion–themed outfit
That’s an en dash there — not a hyphen.
CMOS states: “The en dash can be used in place of a hyphen in a compound adjective when one of its elements consists of an open compound . . .” It adds: “As the first two examples illustrate, the distinction is most helpful with proper compounds, whose limits are made clear within the larger context by capitalization.” Here are those examples plus a non-proper-noun one:
the post–World War II years
Chuck Berry–style
lyrics
country music–influenced lyrics (or lyrics
influenced by country music)
The manual adds: “A single word or prefix should be joined to a hyphenated compound by another hyphen rather than an en dash; if the result is awkward, reword”:
non-English-speaking peoples
a two-thirds-full cup
(or, better, a cup that is two-thirds full)
It does note: “Because this editorial nicety will almost certainly go unnoticed by the majority of readers, it should be used sparingly, when a more elegant solution is unavailable.”
I think you could go without punctuation, if you imagine Haunted Mansion to modify themed outfit. Compare a fabulous themed outfit — no hyphens. Better yet: a Haunted Mansion theme outfit.
Source: The Chicago Manual of Style, 6.80: En dashes with compound adjectives (login required)