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Nonreciprocal microwave devices, such as circulators and isolators, are needed in high-fidelity qubit readout schemes to unidirectionally route the readout signals and protect the qubits against noise coming from the output chain. However, cryogenic circulators and isolators are prohibitive in scalable superconducting architectures because they rely on magnetic materials. Here, we perform a fast (750 ns) high-fidelity (95%) quantum nondemolition readout of a coherent superconducting qubit ($T_{1}=52$ $μs$, $T_{\rm{2E}}=35$ $μs$) without any nonreciprocal magnetic devices. We employ in our readout chain a microwave-controlled qubit-Readout Multi-Chip Module (qRMCM) that integrates interferometric directional Josephson devices consisting of an isolator and a reconfigurable isolator/amplifier device and an off-chip low-pass filter. Using the qRMCM, we demonstrate isolation up to 45 dB within 13 MHz, when both directional devices are operated as isolators, and low-noise amplification in excess of 10 dB within a dynamical bandwidth of $10$ MHz, when the reconfigurable device is operated as an amplifier. We also demonstrate using the variable isolation of the qRMCM an in-situ enhancement of the qubit coherence times $T_{\rmφ}$ and $T_{\rm{2E}}$ by two orders of magnitude (i.e., from $T_{\rmφ}=T_{\rm{2E}}=0.5$ $μs$ to $T_{\rmφ}=90$ $μs$ and $T_{\rm{2E}}=50$ $μs$). Furthermore, by directly comparing the qRMCM performance to a state-of-art configuration (with $T_{\rm{2E}}\approx 2T_{1}$) that employs a pair of wideband magnetic isolators, we find that the excess pure dephasing measured with the qRMCM (for which $T_{\rm{2E}}\approx T_{1}$) is likely limited by residual thermal photon population in the readout resonator. Improved versions of the qRMCM could replace magnetic circulators and isolators in large superconducting quantum processors.