If I want to log two hours of cross-country flight time on a given day, which I will do regardless of having a passenger, is it against regulation to let that ride-sharing passenger pick the destination and split the bill?
A different set of facts might be able to be judged as legal.
You: The weather is great this Saturday for 200 miles in every direction. I'm going flying for currency purposes. Anyone want to come along? Other: I want to go to Martha's Vineyard this weekend. You: I've heard there's a great restaurant on the airport there and I've always wanted to go. I've decided (just now) that I'm flying specifically to MVY this weekend. Would you like to come? Other: Yes. Can I pay for gas? You: Only half of it, because as a private pilot, I must pay my pro-rata share.
If you did that, you're skirting right on the line, but I think you're legal.
If the conversation goes like: You: The weather is great this Saturday for 200 miles in every direction. I'm going flying for currency purposes. Anyone want to come along? Other: I want to go to Martha's Vineyard this weekend. Could you take me? You: Sure; I'd love to do you the favor of taking you to someplace that I hadn't already decided to go! Other: Great. Can I pay for gas? You: Only half of it, because as a private pilot, I must pay my pro-rata share.
That would be clearly illegal, per the FAA counsel interpretation and the demand for a "common purpose" to the trip which isn't met. (Oh, and by the way, isn't required by the FARs either, but it's been a consistent [and reasonable, IMO] policy interpretation.)
I am completely unaffiliated with the FAA, but I suspect that kind of thought process will be involved before they yank your ticket.