Depending on your machine setup you can cut with a 3/8 bit pretty fast:
https://youtu.be/wnBVQkTIng4
This is at full depth. Granted this is a best case scenario here, I'm cutting Luan, I don't care about squareness, and I was just having fun.
For "real" work to keep things nice and square I like to cut with a 1/4" compression in three passes, the first one at .375, the second one leaving a .04" onion skin (and .005 larger than the actual cut I need). Then I come back in reverse and take away that last .04 on Z and .005 and I get a laser finish with just about any bit. Also the parts are dead square (I've also obsessively squared my gantry too)
If you're getting screaming others are right: Slow down your spindle speed and speed up your cutting speed. Personally my safe "always works on plywood" speed is around 4-5 IPS at 12k RPM. Another note on the screaming: Onsrud two flue upsprials always seem to scream somewhat, especially in corners. I've found that compressions (with the right feeds and speeds) don't scream at all.