Generally, yes.
I have had only a couple of issues in mix & match with a given tight rifle chamber where the resizing wasnt quite 'enough', a 'small base' die would have likely done fine but I didnt have one. I just surface ground a few thou' off the shell holder top.
You will probably be just fine.

 

only matters that they fit the press.

 

Brand doesn't matter, your fine.

 

Thanks for the good news.

 

I have a slightly more nuanced answer. There are specialized shell holders that are a couple of .001's off nominal in order to help you adjust your shoulder without adjusting your die. I think Redding sells them in a set with progressive widths. And then there are the "normal" ones that come in one size from various manufacturers (Lyman, Lee, Redding, etc.). There may be slight variations between the thickness of shellholders from different companies. They will all fit your press, and in that sense are interchangeable. But it is more a "pick one and stick with it" kind of interchangeable, rather than "have a bunch in the drawer and choose one at random" kind of interchangeable if you know what I mean.

 

I use all brands interchangeably.

 

They are interchangeable, but I like to use the one that matches the die brand I am using. Thats just one of my things I do.

 

Guess nobody's heard of Herters. They do not interchange. Actually, there were two types. But you can purchase an adapter that allows you to use the RCBS type.

The progressives use shellplates, of course.

Most manufacturers use the same clearance spec - top of shellholder (contacts die body) to shellholder seat. But sometimes there are subtle differences. Can sometimes take advantage of this when dealing with a minimal spec chamber.

 

Hornady case trimmer requires Hornady shellholders. It's the inside diameter. That is the limiting factor.

 

I use rcbs, lyman and hornady in lyman and rcbs presses without a glitch. Never seen anyone post they didn't fit. I've seen posts about lee shell holders not fitting a few times but that doesn't seem to be the norm.

 

I use an Rcbs primer tool and a LeeCT. I think the Lee holders sometimes are a problem with primer tool.