Let's assume the user does not have valid credentials. The problem is here:
if (email.length < 4) {  // <== this gets executed
  setError(true);
}
if (password.length < 5) { // <== this gets executed
  setError(true);
}
console.log(error); // <== still false even after setting it to true
if (!error) { // <== this check runs before setError(true) is complete. error is still false.
  console.log("validation passed, creating token");
  setToken();
} else {
  console.log("errors");
}
You are using multiple if-checks that all run independently, instead of using a single one. Your code executes all if-checks. In one check, you call setError(true) when one of the conditions is passed, but setError() is asynchronous. The action does not complete before the next if-check is called, which is why it gives the appearance that your value was never saved.
You can do this more cleanly with a combination of if-else and useEffect instead: https://codesandbox.io/s/dazzling-pascal-78gqp
import * as React from "react";
const Login: React.FC = (props: any) => {
  const [email, setEmail] = React.useState("");
  const [password, setPassword] = React.useState("");
  const [error, setError] = React.useState(null);
  const handleEmailChange = (e: any): void => {
    const { value } = e.target;
    setEmail(value);
  };
  const handlePasswordChange = (e: any): void => {
    const { value } = e.target;
    setPassword(value);
  };
  const handleSubmit = (e: any): void => {
    e.preventDefault();
    if (email.length < 4 || password.length < 5) {
      setError(true);
    } else {
      setError(false);
    }
  };
  const setToken = () => {
    //token logic goes here
    console.log("setting token");
  };
  React.useEffect(() => {
    if (error === false) {
      setToken();
    }
  }, [error]); // <== will run when error value is changed.
  return (
    <div>
      <form onSubmit={handleSubmit}>
        <input
          type="text"
          placeholder="email@address.com"
          onChange={handleEmailChange}
        />
        <br />
        <input
          type="password"
          placeholder="password"
          onChange={handlePasswordChange}
        />
        <br />
        <input type="submit" value="submit" />
      </form>
      {error ? <h1>error true</h1> : <h1>error false</h1>}
    </div>
  );
};
export default Login;