Re: Where do we draw a line? Signature campaigns or shilling campaigns
Are there any specific rules for operators?
See: Signature Campaign Guidelines (read this before starting or joining a campaign).Quote
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Can they threaten campaign positions for content that is not actually dangerous to anyone, just like the OP?
Yes, of course 
"If you post about Kitchenaid mixers again, I'll stop paying you" is a perfectly fine deal. Take it or leave it.Quote
Did the OP really go out of their way to recommend Sparrow, or did they just participate in normal conversation?
I don't think OP was talking about himself.Quote
If I have a signature for Bitcoin Core and someone asks "what is everyone's favourite wallet?"
Does that mean I have to say Bitcoin Core even though my honest preference is Electrum?
That's up to you. Lying is allowed on Bitcointalk.Does that mean I have to say Bitcoin Core even though my honest preference is Electrum?
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If I say Electrum can Bitcoin Core kick me from the campaign rightfully?
Of course. They can choose who they pay or don't pay.Quote
If I say Bitcoin Core instead of Electrum just to keep my signature, isn't there a big problem with that?
You could just say nothing.I've often seen the opposite argument too: if you do say the thing in your signature is good, people say you're shilling. It's a fine line, which is why I don't want to adjust my posting based on my signature.
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Does signing up to a signature campaign now mean that we have to be mindful (or have to compromise) our honest opinions?
I try not to. That's all I can do. I'm glad no one wants to pay me to say Hamilton Beach mixers are better than Kitchenaid mixers 
I suppose my idealistic view of advertising is different then. I don't think advertising should influence speech, period. That just feels what is most right to me...
In the real world, advertising influences pretty much everything around you.