People are growing sceptical of immigration because it is changing the culture of our cities

What exactly do you mean by culture? If you mean mannerisms/attitudes, then we are very very far from that point. And the immigrants coming from the US are at least civil, not like the North Africans going into Europe. Not saying that I support them coming in, but just pointing out that's an invalid argument. If you are talking about other immigrants, cultures change all the time, they have been changing from the beginning of time. The only concern is we should not normalize barbaric cultural practices that fundamentally go against our values.

and increasing the prices of real estate, child care, and other goods.

There is no economical argument for this. Real Estate prices are only increased by wealthy immigrants who buy 2 or 3 apartments and leave. They certainly aren't caused by low-income refugees.