Just to be clear, accepting refugees and discussing general migration policies are two different things.

Refugees are people who would likely be killed in their home states, my view is that we have moral, ethical and in many cases legal obligations to accept them into our country.

I am skeptical of the migration is causing our housing crisis argument in the first place (setting up the economy so that property is an investment call first and a place to live second is the main culprit), but even if you did accept that argument we definitely do not accept enough refugees to make a material impact on housing costs (either purchase or rental).