If you have to ask if it is safe to feed live rodents than the answer is no. Can experienced reptile keepers feed live rodents while limiting the potential for harm to their collection? Of course. should you feed live rodents if your reptile feeds off frozen thawed? No. If your reptile refuses frozen thawed are you a horrible person for feeding live? Absolutely not.
However and this is advice from experience talking...
If you do not know what you are doing with a fully grown live rodent in a confined space with your precious pet then don't do it. You can find enough horror stories of someone leaving a live rodent in their snake cage, walking away only to come back to a chewed up snake and a very expensive vet bill. If your snake will eat frozen thawed rodents, do that. If not and you must feed live, the best option is to pre kill it yourself before offering. If you can't do that then NEVER leave a live rodent, once it is grown and has the teeth to do damage, unattended in your snake's cage and never just drop a live rodent into a cage without the snake being prepared to strike.
Because you can do something does not mean you should. Why would you take the chance of wasting hundreds of dollars and immense stress over harm to your snake simply because you are either ignorant about what a rodent can do or arrogant about your snake being some killing machine?