All the reports of the Em Drive are not conclusive. The force that they are measuring is very small and very close to the experimental error. It looks more like involuntary p hacking that a good incontrovertible experiment.
I was not following the resents advances of the LENR. IIRC they heat a device with an electric current and they estimate how much heat it release. Measuring heat is a very difficult task, so the measurements are problematic. The additional heat is not too much. They don't have a device that can autosubstain the reaction, and that can silence all the critics.
If you want an to see how the physic community reacts to an anomaly, consider the high temperature superconductors. They are clearly impossible, well at least unbelievable, and the old theory forbid them. But 20 years ago they gave a foolproof method to build a high temperature superconductors in a good lab. The experiments were conclusive. You can even tweak the recipe and get a better superconductor. You can put them under high pressure and get more temperature. You can make many experiments with them. But still there is no good theory to explain how they work. Someone told me that the explanation was flux pinning, but apparently it still disputed and perhaps that explanation is wrong. But anyway, in spite there is no good theoretical explanation, you can make conclusive experiments with an relatively easy to build superconductor and some liquid nitrogen.
Mainstream physics love anomalies. You can get a Nobel price for confirming or explaining it. You can enclose a few graduate students to study it. You can get money from grants. But you must have to ensure a minimal probability that the anomaly is real, because you must release the graduate students someday ...