A flexible coherent passive optical network (FLCS-CPON) is a promising solution for the future access network. By offering increased speed, sensitivity, and flexibility, it enables more efficient utilization of network resources and allows for serving a larger number of users. However, the past studies often overlook the flexibility of channel equalization. In the FLCS-CPON, customized rate optimization has been achieved to cater to users in different channel conditions. However, in addition to rate optimization, further performance improvement can be achieved by providing customized equalization methods. In this work, we proposed and demonstrated an end-to-end (E2E)-optimization-based FLCS-CPON in a 50 km fiber transmission. It enables tailored signal constellation shaping and equalization, maximizing system efficiency and performance. Finally, we achieved a FLCS-CPON with the net data rate (NDR) varied from 124 to 210 Gbps and the power budget of 40 and 42.4 dB in upstream and downstream, respectively; 3.7 and 2.9 dB power budgets are improved by E2E optimization. In burst-mode, the dynamic range of probabilistic shaping 32 quadrature amplitude modulation (PS-32QAM) at a line rate of 250 Gbps improved by 6.1 to 16.8 dB. Additionally, a dynamic range and net-rate product (DRNRP) of 5779 dB · Gbps is achieved.