> Are we to understand that 'dangerous Islamist refugees' are going to vote for liberal and progressive political parties once they arrive in the West?

As the political parties are currently configured, yes. Dangerous Islamist refugees will vote for them for two reasons:

1. "Liberal and progressive" parties are generally the parties of directly giving out money to "the poor", which gets them votes from the demographics receiving the money.

2. "Liberal and progressive" parties in the West are currently overtly pro-Islamic as a contrast to their hated rivals who are "Islamophobic".

What people often fail to consider (in my experience) is that as the liberal and progressive parties draw more of their votes from this kind of group, their party platform will change. Here is a highly stylized thought process that I'd like to argue against, as applied to the USA:

1. Mexicans, when they do bother to vote, vote Democratic by healthy margins.

2. Therefore, more Mexicans over time means a larger vote share to the Democrats over time.

3. Therefore, more Mexicans in the US means Democrats will win more elections and more Democratic priorities will come to pass.

(2), and therefore also (3), are false. The structure of the US political system is that each party gets 50% of the votes. If demographics shift, it can never happen that the parties stabilize at 60% vote share to the Democrats, 40% to the Republicans -- the party platforms will change until each party has 50% of the votes. Packing the electorate with Mexicans will tip the scales toward more wealth redistribution, a current Democratic priority. But it will tip the scales away from environmentalism, also a current Democratic priority. Environmentalism is not a priority for Mexicans in the US.

All of which is to say that "dangerous Islamist refugees" will definitely vote for the parties that are currently the "liberal and progressive" parties, but those parties will become less liberal and progressive in the process.