A series of conjugated microporous polymers (CMPs) based on bromophenol blue (BB) and bromocresol green (BG) have been synthesized via the Sonogashira–Hagihara cross-coupling reaction with surface areas of up to 747 m2/g. The CMPs can be post-functionalized with chlorosulfonic acid to yield corresponding sulfonated polymers with a high acidity of up to 7.67 mmol/g. The sulfonated CMPs showed excellent catalytic activity for the esterification of free fatty acids and transesterification of various vegetable oils and waste cooking oils as well as excellent reusability of up to four consecutive runs without significant activity loss. These sulfonated CMPs have potential applications as recyclable acid catalysts for environmentally friendly biodiesel production from waste cooking oil.