I can't think of any time that if you used a published starting charge you would get into any trouble by switching bullet manufacturer's as long as you stayed in the same bullet weight.

That is to say or shall I say clarify:
If a book says that you use 20.0 grains of H4064 as a starting charge with a 60 grain Speer bullet, you could substitute a 60 grain Hornady bullet.

Is this what you are trying to determine?
Do no substitute powders like IMR4064 and H4064 nor 60 grains bullets up or down to say a 55 or 70 and you should be ok.

Substituting a BT could cause problems as it increases pressure outward at the base of the bullet, but since you are at starting powder charge you probably still won't see any problems.

I commonly look at several load manuals to determine a starting load to make sure also that you haven't got a mis-print.