Was Zachary Taylor a Republican?

The Republican Party as we understand it today didn't exist in Taylor's time, so no, he wasn't a Republican. He was, however, against the expansion of slavery into the Western territories, and this would be a flagship policy of the Republican Party founded four years after Taylor's death.
Politically-speaking, Taylor was a bit of a maverick, a man of independent judgement who resisted being identified with any one party. Prior to his election as President, he'd never even voted. Due to his status as a war hero, Whigs and Democrats alike wanted Taylor to represent them on the ballot in the 1848 Presidential Election. However, Taylor was initially reluctant to commit to either side, and this almost cost him the chance to be nominated. As it was, the Whigs managed to convince Taylor to be their nominee for President, with Millard Fillmore—who would succeed Taylor as President after his untimely death in office—as his running-mate.