I'm driving a TXB0104 translator from 3.3V logic on the B side, VccB is 3.3V, VccA is 2.5V, OE is on VccA. Both supplies are solid. It's on a breadboard. (https://www.sparkfun.com/products/11771). The A-side gave really bad waveform at 1.5MHz while there is no load on it. All 4 channels behave the same. Is this translator broken or just not cut out for 1.5MHz?
To allow automatic bidirectional translation, the TXB has deliberately weak output drivers so that other devices can override the voltage level.
High frequencies require high drive strength, so it has edge accelerators that increase the drive strength during transitions. To allow 100 Mbps, the accelerators are active for only about 10 ns. This means that the capacitance of your circuit must be small enough so that it can be (dis)charged in this time (see section 8.3.3 of the datasheet).
Your waveforms show that the accelerators have timed out before the voltage has reached the rails, so your breadboard, cables, and oscilloscope probes apparently add too much parasitic capacitance.
If possible, use shorter cables, and avoid adjacent breadboard contacts. If that does not help, use a different translator; if your signals are unidirectional, you can use some 74LVCxTxxx chip where you do not have drive strength compromises.