I don't know whether Robinhood as a stock would be worth investing in (probably, but that's your decision to make).
As far as adverse press and reputation are concerned, these sorts of things only have a negative effect if they represent some kind of underlying/fundamental issue with the company.
Unless if you think that Robinhood will repeatedly be hit by regulatory fines, and that the fines or other actions are large enough to strongly impact their bottom line, the FINRA action probably isn't much of a factor.
Do you think the size of those piles of money is priced in? The size of the fear of the size of those piles of money?
The PR related stuff seems easier to figure out.
It's either a great idea or a terrible idea, and I can't tell.