1994 jeep wrangler 4.0 idles fine but when traveling cuts in and out and backfires when accelerator is pushed, i do have a cold air intake and jet performance module just recently added

run the fault codes
check ignition timing is not too far advanced
have a compression test done to check for valve seat insert loose.

change or clean intake air idle control

similar problems: After 20min cool down jeep was bucking/lurching that I traced to bad o2 sensor in exhaust manifold (which you've replaced is seems). The second problem of bucking/lurching, backfiring under certain driving conditions I traced to the battery sliding into the computer wiring harness, disrupting sensor input / output signals. I cured this problem by placing a 1" spacer on rear battery clamp, pushing the battery forward. Been years and no return of problem.

Here are the common cause of surges, stalls at stops, slow idle speed, erratic idle, it is in most cases the idle speed control air-bypass valve and/or throttle valve and upper intake, these area's get full of gunk and combustion residue over the miles and cause idle issues (stalls, low idle) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving

check the injectors and make sure there is fire on those plugs in 3 and 4

Check intake air temperature sensor or MAF sensor. Also check MAP sensor and replace if necessary.

Sounds like a vacuum leak.

Hi,
This is a broad spectrum of possibilities. I would first start with a simple approach of insuring good gas.
When these symptoms occur, get a bottle of fuel additive and add to your tank. Possibly you have some condensation issues. This could be just the ticket... I hope so. Good luck.

timing belt

Fairly common problem. Typical scenario is start vehicle, runs fine for 15 to 30 seconds and begins to backfire when placed under load as customer tries to drive vehicle. Flooring usually makes the problem go away. Usually does not throw a code.

Fix is to replace the upstream 02 sensor.