Certainly they can and they should be able to hire whoever they want. The problems come in when this is done under the table to avoid taxation on both parties. Or, a worker from another, poorer economy may accept a lower-than-minimum wage, which also impacts tax revenue. Instead of spending domestically, they often times send the $$ back home, further reducing domestic GDP. Domestic labor are less competitive and then more people claims welfare and unemployment benefits in a already indebted economy. This is precisely why EU was always a bad idea and Britain voted to BREXIT. To have a true free market, both Taxes and Welfare should NOT exist as a public good (or service). If there are no taxes, theoretically the market will be more optimum, because all government interventions, including taxation, result in a dead weight loss. But if there were no taxes, there could be no welfare nor public services, which many welfare economists argue that it would lead to increased crimes and social unrest. That's not good for the long run. If you speak to welfare economics professors, they will *probably* tell you something about sacrificing efficiency to reduce crime...etc, but that's a totally different topic and is out of my expertise so I will not comment on that. However, if you are interested to learn more about the impact of taxation, read this paper by NBER:
In addition, for the Nth time, I am not against immigrants who come here to work and contribute to the society. I was specifically against those who come here to leech on social welfare and be a "free rider". The problem becomes exacerbated when those free riders come in and bring even more free riders to us. All the liberal ideals would have worked if everyone did their part, but unfortunately people, not all, but some of those from poorer nations, are very, very self-centered and would not think twice about taking advantage of another person's wealth.