The reason I would have some doubts is they were talking recently about providing checking and savings features like a bank, only tied to a brokerage account, and they said cash therein would be SIPC insured and the SIPC had to contradict them publicly and say "nuh-uh".
This doesn't indicate your stocks aren't safe per se, but it suggests that Robinhood may not always verify that something is 100% ok with regulators before doing it, or think about all the implications, and some day we might find out "oops" they didn't do something crucial that traditional brokers do, because they were being disruptive, moving fast and breaking things.
Another point is that while Robinhood Financial appears to be a more or less normal broker that is a member of FINRA and SIPC, Robinhood Crypto is not. This isn't exactly surprising, but again, it could make a person slightly nervous that there could be drastically different consequences someday to trusting different entities that are all called "Robinhood". Maybe people will get used to trusting both of them and someday there will be a new "Robinhood XYZ" and it will not be regulated the way people expect. Or what if when Robinhood Crypto is hacked and loses their customers assets, it turns out there is some linkage that causes problems for Robinhood Financial, even though it wasn't supposed to work that way.