IMO . . . you do not get the "power" out of a rechargeable CR123,or the longevity out of a rechargeable CR123.
I buy them on line for $.96 - $1.00 each. None of the saving the batts,finding them at the bottom of my backpack,digging out the charger,etc,etc.
The ONLY rechargeable batts that I use are the 18650's. They are the 5000mAh batts and even finding downed animals and the like,only have to recharge them every third hunt or so. --- SAWMAN
It comes down to a voltage issue. Some items can be damaged by improper voltage and some just don’t perform as well with it. Not much upside. Plus rechargeables don’t handle the cold as well in my experience.
I recommend you read the manual/instructions that came with your various battery operated devices as to whether rechargeables can be used. In the case of my handheld/clip-on/standalone thermal, it says they can be used. I've been using Tenergy RCR123A's for several years. Where a quality CR123A like Panasonic will run that thermal for 3-4 hours, the rechargeables run it for about 1 1/2 hours. With non-rechargeable batteries when I get the low battery warning light, I have about 10-12 minutes before the thermal goes dead. With the rechargeables the thermal goes dead in less than 5 minutes when the low battery warning comes on.
If your unit can use rechargeable, then it's up to you to decide the cost vs benefit vs performance aspects and make your decision. If I have a guest with me, I always use name brand 123's to get the longest run time without the annoyance of sooner battery swaps/down time. If I determined I'm going on a stalk (and have the time), I pop in fresh batteries. I get my 123's from Batteryjunction.com. I go together with friends and get bulk buys. They also send coupons for % off.
Note: When a rechargeable 123A comes fresh off the charger, the volts can be a bit higher than after they've sat a little bit. I don't know if that can hurt the equipment, so MY procedure is to let them sit 30 minutes or so before using them to give them time to "settle down". Easy to check yours...just test the volts right after charging with a multimeter, then 10 minutes later, then 10 minutes later to see how yours behave.
I mentioned buying in bulk. I also use Titanium brand Chinese 123A's. A little less capacity than "name brand", but when I do the math, the cheaper price means less cost per run time.