Sure but Anti-Democratic can mean against the party or against democracy. Anti-Democrat while technically incorrect is clearer.

The epithet 'Democrat Party' has been used for over a hundred years to refer to the Democratic Party. https://en.wikipedia.org/wiki/Democrat_Party_(epithet)

The slur stems from how the Democratic Party campaigns on democratic principles and helping the people, but when in elected they end up not delivering and instead protecting donors & corporate interests. They also do not act democratic. The Democratic Party rigged the 2016 primary so Bernie Sanders would lose to Hillary Clinton. Then in 2020 they rigged the primary again so Joe Biden would win against Bernie Sanders. Then in 2024, they rigged it again so Kamala Harris became Democratic nominee without winning the primary. All of this was done to protect donor & corporate interests.

The Republican party is the same, there's nothing republican about them.