Okay, I've been using various brands of lead free (compressed powdered copper/tin core) jacketed varmint bullets since 2007 when California went lead free in the condor zone. The brands and specific bullets I use are:
.204 Caliber:
Barnes 26 grain Varmint Grenade
Hornady 24 grain NTX
Nosler 32 grain BT Lead Free
.224 Caliber:
Barnes 36 Grain Varmint Grenade (Usually stabilizes in 1:12" or 1:14" twists).
Barnes 50 Grain Varmint Grenade (Requires 1:10" twist with 1:9" or faster better in all cartridges including .22-250)
Nosler 40 grain BT Lead Free
Speer 50 Grain TNT Green (insufficient accuracy all tested loads).
I didn't get really great results from the Hornady offerings in lead free varmint bullets.
.243/6mm:
Barnes 62 Grain Varmint Grenade
Nosler 55 Grain BT Lead Free
.257 Caliber:
Barnes 80 Grain TTSX (this is not a frangible bullet, but the only good choice in a .257 Roberts or AI, also for the .25-06. Accurate but expensive, blows ground squirrels up, and is ideal for deer/pigs/pronghorns).
.308 Caliber:
Barnes 150 Grain MPG (This is a big Varmint Grenade with a cannelure. Very accurate in a 1:10" twist).
Below: Two 10 shot test groups from a .204 Ruger AR-15 BOLT ACTION rifle built on a side cocking upper with no gas system, using a Hart custom made 1:9" twist heavy barrel. This rifle is a home build designed not to toss brass in the weeds. The red diamonds are .5".
Below: A sight-in target from my standard load fired in a Savage .204 Ruger built on a Savage Precision Target Action, 1:12" twist Shilen, 24" Varmint contour barrel. The group includes two scope adjustments from right to left. Load was 25.2 grains of Rl-10x, Winchester brass, WSR priner. The rifle was another home made "hope for the best" rifle. Velocity 4,110 fps.
Below: Best .223 Remington group using the Nosler 40 grain BT Lead Free bullet in a Pac-Nor 1:9" twist polygonal barrel on a Savage Dual Port Precision Target Action. That's 10 shots at 100 yards, no wind, overcast day. This load killed lots of Oregon sage rats, cool thing is the plastic tip separates and blows a hole somewhere near the rat's head when shot in the chest.
Below: A 9 shot group with the Barnes 36 Grain Varmint Grenade, in a 1:10 twist. This bullet is best for rifles with slower twists, less than 1:10". I didn't count the first shot as I touched the Jewel Trigger a bit too hard, firing on the way to the aiming point. Average velocity 4,018 fps.
Below: Same rifle, with Barnes' 50 grain Varmint Grenade. The Pac-Nor 1:10" twist didn't stabilize this long bullet as well as subsequent 1:9" or 1:8" twists, but maybe I'm too picky. Average velocity 3,662 fps.
Below is the 6mm Barnes 62 Grain Varmint Grenade from a 1:8" twist Pac-Nor barrel. The best this rifle ever shot was a .187" 10 shot group at 100 yards. I stopped annealing and neck turning the cases as doing so wasn't worth the minuscule accuracy gain, if any.
Keep in mind that lead free bullets like faster twists, and some barrels are not the exact twist they are rated, usually being a bit slower. And they like to be seated away from the lands.