I've had what I thought were pretty constructive and interesting conversations about this topic right here on Hacker News.
Maybe you could talk about smaller and more specific aspects of the issue with people, like
* How has present-day opposition to immigration in the U.S. developed? Was there always strong anti-immigrant sentiment in this country? How were immigrants viewed in different eras? Were parts of those views accurate or inaccurate?
* What are the moral arguments in favor of people's right to migrate? What are the moral arguments in favor of a nation's right to prevent or limit migration? Is it important what existing citizens of a country think? Is it important why they think it?
* Is the present-day international system of nation-states and borders a good idea? How about various notions of citizenship? Are some criteria for citizenship obviously reasonable or unreasonable? Should criteria for citizenship be decided politically by existing citizens or are some kinds of decisions they might reach clearly unfair or morally wrong?
* Should people who live in a country feel proud that others want to move there? Should they feel proud of allowing or encouraging others to do so?
* Why are so many economists so strongly in favor of unrestricted or nearly unrestricted migration? Why have other people found the economists' consensus hard to accept?
* How do immigration restrictions interact with policy mechanisms like a welfare state and minimum wage?
* Is it good, bad, or neither for a government to favor the interests or preferences of existing citizens over others' interests? If it's not bad to do so, are there clear limits to how or to what extent the government may neglect or override foreigners' interests?
* What do we think about cultural differences between people living in different parts of the world? Would we like to acculturate as many people as possible to our own culture and way of life if we had the opportunity? Do we think that acculturation of this sort is inherently good? Do we think existing cultural differences are good, bad, or neither, and do we think at least some cultural differences can be placed on a hierarchy where one culture gets something more right than another?
* Are immigration critics right to worry that a culture could be made worse (and in some way less effective) by the arrival of lots of people with different cultural values? Are immigration supporters right to hope that a culture could be enriched by the arrival of lots of people with different ideas and traditions?
* Is there a meaningful moral difference between trying to deport existing residents who entered a territory without following its official migration rules, and trying to prevent other people from doing so in the future?
* What are the differences between population growth through migration and population growth through reproduction? Doesn't this undermine a simple intuition that migrants take away jobs from existing residents?
* How legitimate is it for members of an ethnic or cultural group to want to have their own nation-state and to make that nation-state somehow reflect the character or interests of that group rather than other groups?
* Is it true (as an article recently posted to HN suggested) that migration almost always makes the economy bigger and creates more total employment, but that the benefits of this growth may be quite unequally distributed or captured? Could migration economically benefit most people while economically harming some people?
* To what extent should a country try to assimilate migrants and to what extent should it be proud of having done so? Are there likely problems if large-scale migration happens without a corresponding assimilation? How successful has assimilation been in the past? Is there something legitimate in the preferences of migrants who don't want to assimilate (or only want to assimilate a little bit)? Is there something legitimate in the preferences of people who strongly want migrants to assimilate?
* Is there some kind of hypocrisy in creating or enforcing significantly stronger immigration restrictions today than those that prevailed in the past?
* Are there reasons for migration that are more or less important than others? How much should discussions about immigration address migrants' motivations? Are there motivations that change the moral status or significance of someone's desire to migrate?
* Many governments have created programs that try to draw distinctions among would-be migrants on the basis of their desirability. Have these programs worked well on their own terms? Who proposed them, and who got to create the criteria for desirability?
* What could governments reasonably know or ask about visitors or would-be immigrants?
* How much migration might occur if practical restrictions on it were removed? What might the long-term consequences be?
* If it's legitimate to physically restrict some kinds of immigration, what kinds of enforcement measures are proportionate and should people be punished somehow for circumventing or attempting to circumvent them?
* What if a country allows people to immigrate easily but makes it difficult or impossible for them to acquire citizenship? (How about temporary "non-immigrant" work visas?)
I bet there are about a dozen more things that could be discussed in this area.
I mention these things because I think it's possible to learn something from talking about them with people who radically disagree with you (and you don't have to give up your moral outlook on the situation, nor your political goals!).