OK non-believers let's look at the manuals. Take the .270 Win for example using IMR4350 (I selected a popular caliber and powder)
Speer #8: 130 gr Spitzer; Starting load 52 gr. Max 56.0 (Case Remington)
Lyman 46th ed: 130 gr Spitzer; starting load 49.0, Max 54.5 (Case Winchester)
Hornady Vol II: 130 gr Spire; Starting load 51.6, Max 57.6 (Case Western)
Sierra: 130 Spitzer; Starting load 48.4, Max 54.9 (Case Remington)

So based on my initial post of not loading to maximum charge. My favorite .270 load with 130 gr Hornady Interlock or Sierra Spitzer was 54.0 gr of IMR4350. This load is below the maximum charge for any 130 gr jacketed bullet using any case.
Ergo using mixed brands is not dangerous under these circumstances. The only thing that will suffer is a decrease in accuracy which will not be noticed unless shooting at extreme distances. This load with my Rem 700 which would shoot sub MOA all day long was responsible for killing a few whitetails at 300 yds, a couple antelope at 200 - 300 and one muley buck at 437 yds and I don't know how many whitetails at <100 yds.