I’ve moved all of my money to Charles Schwab. I presume they can’t touch investment money? (Comments?)
Anything's possible down the line. But as of now, your money is safe, whether it's in the local bank or with Charles Schwab. It's not tin-foil hat time there yet.
The problem is that any interest rate move will affect all invested money everywhere, in a Schwab account or not. So if the Fed rate goes negative, your Schwab money market rate will drop, maybe to 0%. I think that folks like Schwab will try to avoid going negative as long as possible, just for PR reasons.
On the other hand, a rate drop will make any long-term bonds you have with Schwab (or with anyone else) more valuable.
As for stocks, eh, who knows?