I know very little about #1's, but I have one in 7x57. When I eject a fired shell it catches on the safety and stays in the action. Anything I can do about that?

That's pretty normal with my experience of owning three No. 1 Rugers. I actually like it because I don't have to chase the brass.

Problem is common to the #1. Turn the rifle to the side as you eject the case. The d@nm safety sticks up a little too far. There is an aftermarket safety fix for it, but most of us get used to turning it a little.

You can taper the front edge of the safety, replace it with an aftermarket one that's tapered, or tip it to the side like the man said.

The classiest fix involves recessing the button into the tang, but I'd only do that on a custom build as it'd probably cost a couple hundred bucks. It is very handsome, however.

I figured out the flip to the side way back when I was a kid

Did it ever occur to anyone to Read the Instruction Manual!
In the Manual it clearly states that you can adjust the spring tension on the extractor/ejector to have the Cartridge just eject partially or kick them out with enough force to throw the spent cartridge several feet.
Not a problem.

Wow...wish I had thought of that years ago...

Sure, adjusting the tension down is great when you want the case to just flop out and lay in the trough. Great for varmints or plinking / target practice.

But when you want the case to clear for a faster reload, it doesn't matter how much tension you add to the ejector spring, the case hits the safety and bounces forward. I've even had them bounce back into the chamber before. At least until I got in the habit of tilting when ejecting.

I have contemplated having an aftermarket safety installed but just can't seem to get around to actually having it done...just not important enough I guess...I'll likely just keep tilting.

Straight walled rimmed cases are worse, but like someone, it makes brass retrieval much easier.

And really think about it...when did you ever need a super fast follow up shot? If you ponder second shots you will usually recall that its a matter of minutes between shots, not fleeting seconds.

And if the seconds look like they're going to fleet, turn the rifle sideways and get busy!

Having purchased my first Ruger No1 in Oct 1967 and owning over 200 of them in my lifetime and never had a problem with the Safety I think you are full of it.