Hi Wendy,
You're absolutely right! "Respectively" is unnecessary in that sentence because there's no ambiguity—the subject ("I") applies to both dislikes equally.
The best way to combine your sentences naturally would be: "I'm not big on Western cuisine or parties." or "I'm not really into Western cuisine or parties."
"Respectively" is usually used when matching two separate subjects to two separate objects, like: "John and Sarah are not big on Western cuisine and parties, respectively." (This means John dislikes cuisine, and Sarah dislikes parties.)
Since your original sentence only has one subject ("I"), there's no need for "respectively." 👍😊