The unprecedented highly cis-1,4 selective (>99%) coordination–insertion polymerization of the polar monomer 2-(4-methoxyphenyl)-1,3-butadiene (2-MOPB) has been achieved using a β-diketiminato yttrium bis(alkyl) complex to afford a hydrophilic plastic polymer P(2-MOPB) with a water contact angle of 87.7° and glass transition temperature of 34.2 °C. The copolymerization of polar 2-MOPB and non-polar isoprene has also been successfully realized for the first time to produce a type of highly modified cis-1,4 polyisoprene with a wide range of 2-MOPB content (8.2%–88.5%). The composition was adjusted by regulating the monomer feed ratio according to the copolymerization kinetics. Hydrogenation of P(2-MOPB) provided an unusual alternating copolymer, poly(4-methoxystyrene-alt-ethylene) that could not be obtained via any other methods.