The U.S. recently became an oil and natural-gas exporter and actually a net exporter. With the oil price declines then West Texas fracking is now at real risk.
But the oil industry is not the dominant industry in the U.S. and so the Ruble is down against the Dollar. Also, neither the Euro or the Swiss Franc should have any particular advantage over the dollar. The U.S. stock market should actually hold on the oil price shock.
Now if the lower oil price pushes inflation lower then the various central bank polices of increasing inflation don't make very much sense. The central banks say that since growth causes inflation that they can then create inflation so as to lead growth. A lower oil price will point towards deflation except that the lower of cost of oil to industry could increase corporate profit margins and increase economic activity.
Oh, the current oil price crash is due to an expected increase in supply and that should not have hurt the stock market. But future oil price pullbacks due to reduced demand, as due to possible epidemic, should hurt the stock market because reduced demand for oil represents reduced economic activity