How to make axios synchronous

You can’t (or at least really shouldn’t) make it synchronous, so you’ll need a different way forward.

One idea: return the promise from Axios:

checkUniqueness () {
    return axios.get('/api/persons/unique/alias', {
        params: {
            id: this.id,
            alias: this.alias,
        }
    })
    .then((response) => {
        console.log('2. server response:' + response.data.unique)
        this.valid = response.data.unique;
    });
}

and then call then() on it in save():

this.checkUniqueness()
.then((returnVal) => {
   // other validations here
  //  save
})
.catch(err => console.log("Axios err: ", err))

You could even do all your checking on one place if you returned the value from Axios’s then() rather than setting the flag:

.then((response) => {
    console.log('2. server response:' + response.data.unique)
    return response.data.unique;
 });

then in save:

this.checkUniqueness()
.then((valid) => {
    if (valid) // do something
   // other validations here
   //  save
})