We see in The Half Blood Prince that Horace Slughorn boasts of having the best among the Hogwarts students in his Slug Club through the years.
Is there any instance of anyone declining (or trying to decline) the invitation to join the club?
(Inspired by this comment)
Aside from Harry who wouldn't have gone if Dumbledore hadn't told him to, no one is recorded as rejecting an invitation (even if they didn't want to go, like Hermione).
"Anyway," said Hermione, continuing their interrupted conversation as though a lump of wood had not just attacked them, "Slughorn’s going to have a Christmas party, Harry, and there’s no way you’ll be able to wriggle out of this one because he actually asked me to check your free evenings, so he could be sure to have it on a night you can come."
Half Blood Prince — Chapter 14: Felix Felicis
"Harry, that’s three of my little suppers you’ve missed now!" said Slughorn, poking him genially in the chest. "It won’t do, m’boy, I’m determined to have you! Miss Granger loves them, don’t you?"
"Yes," said Hermione helplessly, "they’re really –"
"So why don’t you come along, Harry?" demanded Slughorn.
"Well, I’ve had Quidditch practice, Professor," said Harry, who had indeed been scheduling practices every time Slughorn had sent him a little violet-ribbon-adorned invitation. This strategy meant that Ron was not left out and they usually had a laugh with Ginny imagining Hermione shut up with McLaggen and Zabini.
"Well, I certainly expect you to win your first match after all this hard work!" said Slughorn. "But a little recreation never hurt anybody. Now, how about Monday night, you can’t possibly want to practise in this weather …"
"I can’t, Professor, I’ve got – er – an appointment with Professor Dumbledore that evening."
"Unlucky again!" cried Slughorn dramatically. "Ah, well … you can’t evade me for ever, Harry!"
Half Blood Prince — Chapter 12: Silver and Opals
"Listen, it’s not my fault Slughorn invited Hermione and me to his stupid party, neither of us wanted to go, you know!" said Harry, firing up.
Half Blood Prince — Chapter 11: Hermione’s Helping Hand
(emphasis mine)
Slughorn started the Slug Club as a way for him to get to know and make a good impression on students who are likely to be influential later in life. The entire point of his club was to make these chosen students feel kindly towards Slughorn, so he'd have more influence in getting favors from them.
“He used to handpick favourites at Hogwarts, sometimes for their ambition or their brains, sometimes for their charm or their talent, and he had an uncanny knack for choosing those who would go on to become outstanding in their various fields. Horace formed a kind of club of his favourites with himself at the centre, making introductions, forging useful contacts between members, and always reaping some kind of benefit in return, whether a free box of his favourite crystallised pineapple or the chance to recommend the next junior member of the Goblin Liaison Office.”
- Harry Potter and the Half-Blood Prince, Chapter 4 (Horace Slughorn)
It seems unlikely that Slughorn would force a student who didn't want to participate to be in it - if only because forcing them to take part in a club they have no interest in is unlikely to make them feel favorably towards Slughorn, accomplishing the exact opposite of his goal of creating the Slug Club to begin with.
In addition, the Slug Club isn't a Hogwarts-mandated class or activity, so students wouldn't suffer repercussions or punishment for not wanting to take part, nor would it likely affect their other studies (except perhaps Potions if they've sufficiently upset Slughorn).
Yes, Harry Potter often refuses Professor Slughorn invitations by 'co-incidentally' scheduling Quidditch practices on the same day.
