The most common and most likely answer to this crossword clue is the 10 letter word IDOLATROUS
I've seen this crossword clue in The Sunday Telegraph
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More clues leading to the result IDOLATROUS
Buddy explains!

The straight part
We know that "Worshipping inappropriately" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case worshipping inappropriately = idolatrous.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does IDOLATROUS mean?
IDOLATROUS adjective- Partaking in idolatry; worshipping idols or false gods.
- Engaging in excessive attachment or reverence; inordinately or profanely devoted.
- Used in or designed for idolatry; devoted to idols or idol-worship.
- Of or pertaining to idolatry.