I personally think most of the assault on lead is greenie hype and BS.
Like BarnesX.308 posted, I always cut out and discard any bloodshot meat. My family and I have eaten game meat shot with lead bullets almost every year since 1965 without any health issues from lead.
I started using Barnes TSX bullets in 2005 when I went on a cape buffalo hunt in Zimbabwe. There is an ongoing debate on whether to use soft point or solid bullets for buffalo, and my PH suggested that I just use a TSX bullet as they offer great expansion and deep penetration. I used a .375 RUM on that hunt and on two hunts in South Africa, and because the TSX bullets perform well and are accurate in that rifle, that is the only bullet that I have hunted with in that rifle.
In 2004 I built a .300 Weatherby, and because the TSX bullets worked good in my .375 RUM, I decided to try them in my .300 Bee. They also shot well is this rifle so I used them on a couple of Western US hunts, and they also performed well on the animals that I shot with them, including a bull elk.
In 2012 while I was preparing for another South African hunt, I could not find any .30 caliber 168 grain TSX bullets, but a local store had 168 gr TTSX bullets, so I bought a box of them. They shot slightly better than TSX bullets had, so I used them in my .300 Weatherby on that South African hunt where they performed very well. I have since used these bullets on another Montana elk hunt and a New Zealand hunt, and again they have performed very well.
I still hunt with lead cup and core bullets in my .257 Ackley and my 7 mm Rem mag, and other than waterfowl where we are required to use non lead shot, I shoot lead shot for upland game hunting.