I know what libertarian academics and economists say about immigration. Curious though the absence of threads here started by libertarians to oppose Trump when they have so many threads to attack other stuff they do not like such as SJWs and such.
Here is a libertarian website that I occasionally post to called
Bleeding Heart Libertarians - Free Markets and Social Justice. Libertarianism is so ill-defined that you can probably find a libertarian who holds any belief that you could name and argues that it is a True Libertarian™ belief.
This makes it hard to generalize about libertarians, but one of the core beliefs shared by most is that the labor market should be a true market where wages are like the prices of commodities that go up and down with supply and demand, in this case, the supply of and the demand for labor. As a part of this belief, one of the factors that would reduce the otherwise strong bargaining position of the employers is that the workers could move to areas where the wages were higher. This includes across borders. Most conservative libertarians, therefore, support open borders, albeit most add the caveat that a nation can only open its borders after it has eliminated all forms of open welfare including Aid to Dependent Children, Social Security, Medicare, etc. so that people are immigrating to work and not to take advantage of the open welfare. (Open welfare is where the government provides cash to the recipients, versus putting them in a poorhouse or a debtors' prison.)
It would follow that most libertarians would oppose Trump's immigration policies, that this is an area where libertarians aren't aligned with conservatives. I haven't seen any real evidence of it here. However, I am seeing some pushback elsewhere from libertarians, but not especially on immigration.
Here is a debate with both a libertarian capitulation to Trump on immigration and more typical traditional libertarian open borders view from Reason magazine, which I am sure that at any moment we will be told isn't a True Libertarian™ magazine.
In past, I have taken our libertarians here to task for just sniping at discussions with one line questions or statements and not telling what they believe, what positions they take and that they are willing to defend. I have come around to a much more benign understanding of libertarians when I finally realized that most have no real idea of what calling yourself a libertarian means. That most haven't read any fundamental libertarian literature beyond Atlas Shrugged or similar, the table of contents of Friedman's Capitalism and Freedom and the comic book version of Hayek's The Road to Serfdom.