I can add 1 item to the array it logs [\"50\"] in the console. But when I try to add a second value I get this error \"currentScores.push is not a f
The return value of currentScores.push() is the new number of elements in the array. You then save this in your state which means that scores in your state becomes a number instead of an array.
You likely want to construct a new array instead since you are working with constant variables:
const currentScores = this.state.scores;
const newScores = currentScores.concat(this.state.scoreInput);
this.setState({ scores: newScores });