There are many conservatives who want no immigration, legal or otherwise.
Really? Can you name them? In all the immigration discussions I've never heard anyone say they were against legal immigration.
Not true. There are a 'few' conservatives that want no immigration period. But 'most' conservatives would now favor a moratorium on all immigration until it is demonstrated that the nation can secure its borders and manage a flow of legal immigrants. Then they will favor legal immigration.
Conservatives do not hate immigrants, they hate a government that is mismanaged and wasteful on any issue including immigration.
So you cannot say conservatives do not want legal immigration, they in fact do want immigration when it is managed properly to fill well-defined targeted needs of the country.
And past generations of conservatives have supported legal immigration in a focused manner. For example, the Lithuanian communities of Detroit and Chigago were started in the early 1900s by an influx of immigrants brought in by the automotive manufacturing industry. Workers were needed and those people had the skills. Their families followed them. Once enough workers were placed, the immigration was cut.
What we have now is an uncontrolled mess.
Conservatives are not against the immigrants, they are against the 'mess'.