Generally speaking I do not use 125/130's for medium game (deer) in any medium or large capacity .30 case. It is inappropriate.
The problem is not bullet wieght but rather bullet CONSTRUCTION. In .30 caliber almost all 125's and 130's are designed to be light for caliber rapidly expanding bullets for use on varmints and little critters. When driven to .308/30-06 speeds these bullets over expand, do so too rapidly, and do not hold together well enough for really good use on deer. Yes. They will work. No they are not recommended.
You can use a 125 softpoint in a 308/3006 in youth loads. When these are loaded to reduced velocities (for lower recoil) the bullets expand somewhat slower, penetrate deeper, and acutally do a better job on deer. I do load a 125 remington SP in such a youth load. Check Hodgdon. THey have published youth loads for .308, .30-06, and others...
As a general rule you can look at any caliber that is between .243/6mm and .30/7.62. If the bullets are light for caliber they are designed, intended and constructed for use on little critters and open too rapidly for good use on deer. If its heavy for caliber its constructed for use on deer and similar large critters. Thus, a 100 grain 243 bullet is likely a decent deer bullet, while a 100 grain .30 bullet isn't.
There are exceptions to the rule. Generally speaking, you can get away with using the light for calibers on deer. However, they tend to work BETTER as velocities are decreased. If you want to find some actual documented experiences using a particular bulllet, look at handgun hunters. Many of them use a variety of bullets in Contenders. Lower velocities mean 'regular' deer bullets are going a little too slow for good performance. They use light for caliber bullets, drive them at modest velocities (frequently 2200 to 2400 fps) and they get the job done well.
I've only been able to achieve modest accuracy using 125 Rem PSP over H4895 in a .308 Model Seven. Recoil was not reduced as much as I had hoped. I ended up buying the daughter a Seven Youth .260, and load a Nosler 120 Ballistic Tip over AA2520 and get 1-1.5 MOA in with lower recoil. THese are moving 2400 fps, and are dead ringers for the much esteemed 6.5 JDJ load. I would not dream of using these 120 BT's at typical 2700-2800 fps speeds. They work well at 2400 but are waaaaaaaaayyyy to fast opening to be used at 2700+