Mixed-precision quantization works Neural Networks (NNs) are gaining traction for their efficient realization on the hardware leading to higher throughput and lower energy. In-Memory Computing (IMC) accelerator architectures are offered as alternatives to traditional architectures relying on a data-centric computational paradigm, diminishing the memory wall problem, and scoring high throughput and energy efficiency. These accelerators can support static fixed-precision but are not flexible to support mixed-precision NNs. In this paper, we present BF-IMNA, a bit fluid IMC accelerator for end-to-end Convolutional NN (CNN) inference that is capable of static and dynamic mixed-precision without any hardware reconfiguration overhead at run-time. At the heart of BF-IMNA are Associative Processors (APs), which are bit-serial word-parallel Single Instruction, Multiple Data (SIMD)-like engines. We report the performance of end-to-end inference of ImageNet on AlexNet, VGG16, and ResNet50 on BF-IMNA for different technologies (eNVM and NVM), mixed-precision configurations, and supply voltages. To demonstrate bit fluidity, we implement HAWQ-V3's per-layer mixed-precision configurations for ResNet18 on BF-IMNA using different latency budgets, and results reveal a trade-off between accuracy and Energy-Delay Product (EDP): On one hand, mixed-precision with a high latency constraint achieves the closest accuracy to fixed-precision INT8 and reports a high (worse) EDP compared to fixed-precision INT4. On the other hand, with a low latency constraint, BF-IMNA reports the closest EDP to fixed-precision INT4, with a higher degradation in accuracy compared to fixed-precision INT8. We also show that BF-IMNA with fixed-precision configuration still delivers performance that is comparable to current state-of-the-art accelerators: BF-IMNA achieves $20\%$ higher energy efficiency and $2\%$ higher throughput.