Most wealthy people get their wealth from the labor of poor people. If poor people have easy lives, and need to work less hard for fun and to enjoy life, then they are less likely to work hard and wealthy people are less likely to stay wealthy.
I can't demonstrate a causal link because it would be impossible to design a study really showing that.
To demonstrate anything, I'd have to get a group of wealthy people and determine which of them don't want poor being free (and just asking them wouldn't reveal that).
Then I'd have to determine which of the wealthy people hate e-bikes by asking them.
Then I would have to see if there was a correlation.
If you use Democrat versus Republican as a proxy for the first inquiry, it would be an easier but less approximate estimation.
In order try to show causation (and it would be a iffy showing), you would have to take wealthy people and measure their views of e-bikes, wait a week, divide them in three, and show them films of poor people. One film would show poor people disliking ebikes and being unhappy. One film would show poor people feeling free after using ebikes and having nicer lives. One would be a film of a a film that showed something as neutral as possible, like a show about how to do math problems. That wouldn't actually be neutral, so if a budget allowed there would be a fourth group with no tv show at all. Then measure their views of e-bikes again and see if they changed.
I can't prove any of this, but the wealthy people shown groups of poor people happy using e-bikes would probably have more negative views of e-bikes after on average because this is a control issue. E-bikes are cool and great for the planet and rich people who don't like them only have 1 rational reason: wanting to maintain their lifestyle and concern that the lower classes finding more fun may reduce that. (And alcohol is fun and promoted because lower classes who use it a lot are more likely to have less intelligent children who will lack social mobility and can be exploited more easily.)
So yes, I don't have a budget or inclination to prove this, but it's not an impossible thing to prove nor is it irrational.