While I'm not aware of any engine that has variable pitch compressor blades, variable pitch stator blades have become pretty common. This started with the J79.
Here's a link to a RAND Corporation reference to military jet engine development, and the following extract comes from this reference.
jet engine development
The move toward high-pressure-ratio engines first advocated by P&W soon confronted designers with new difficulties. As pressure ratios increased for optimal efficiency at cruise conditions, problems arose with the design of the compressor operating efficiently at low speeds and especially during acceleration. Under these conditions, airflow patterns over the compressor airfoils were very different than they were under their design conditions, and small disturbances that could cause compressor stall became common. GE made the revolutionary technological breakthroughs that solved this problem by developing variable-geometry compressor systems, which used variable-geometry stators. A row of stators redirects the airflow between each row of rotating compressor blades in the compressor assembly. Variable stators change their angle of attack for different airflow conditions, thus addressing the compressor stall problems. This technological breakthrough led to the development of the famous J79 turbojet engine, made Mach 2 flight possible, and was critical for the development of modern very-high-bypass commercial engines that power today’s large airliners.