Is it illegal to work remotely at Goldman Sachs and fidelity investments at the same time?

Yes and no, if you’re licensed at both then you have to get permission per FINRA

Its probably in your employment contract. I doubt it's illegal but probably a forever offense.

YES Both are finance firms and it will be a conflict of interest for you to work at both firms at the same time. You can even get fired from both firms.

It’s a breach of the code of conduct and conflicts provisions. You likely would be fired.

OP asked if it's illegal, not a fireable offense/immoral. I'm also interested in the legality of it. A company's code of conduct is not law.