I've done it with no issues, apart from varied rates of oil consumption. The HM oils do stave off consumption on my Saturn S, a notorious oil burner though mine is better than most.
Best HM oil I used was M1-HM, followed by my current fill of Pennzoil HM. The Kendall HM I got once at Firestone did not slow consumption at all compared to non-HM oil.
But to answer the question: I have used HM, non-HM, dino, semi-syn and full-syn, 5w-20, 5w-30 and looking to use 0w-30 this coming winter. Mobil, Quaker State, Pennzoil and Kendall. My car still runs. No engine issues. As long as the oil meets your vehicle's specs, you keep it topped up and run a reasonable OCI all will be well. Might run a hair smoother or burn a bit less oil or get a tiny bit better mpg with a given oil, but not enough to get excited about.
Except here.