If you are a progressive talking about immigration, please try to frame your messaging as follows:
Immigration is, according to a load of studies, an overall benefit to the economy. But we all know from personal experience that ‘good for the economy’ is not always good for individuals. Immigration can suppress wages, at least in the short term and in local areas, because immigrants are easier to exploit than a lot of other groups. They’re unplugged from any support networks they had growing up, they may not be aware of all of their rights (they may have fewer legal rights), they may miss nuances of language, and so on. And this means that unscrupulous businesses can under pay, over work, and otherwise take advantage of them.
This is even more true of refugees (who literally don’t have anywhere else to go) and people on work visas sponsored by their employers (and so are dependent on their employer’s good will to remain). Work visas that allow partners to come over but not work places more pressure on the single wage earner and makes them even more dependent on their employer.
By creating a class of people that are easy to exploit, unscrupulous businesses can make you directly compete in the labour market with people who have no choice but to accept conditions that you would find unacceptable.
If you’re worried about immigrants taking your jobs, the solution to this is to provide stronger worker rights for immigrants and big penalties for any employer who is found to have violated minimum wage laws. It’s to end loopholes where people act as employees but have the rights of self-employed workers. It’s to make sure that people on high-skills visas can easily move jobs and must be paid a fair market wage.
When someone is demonising immigrants, it’s because they benefit from having an exploitable underclass. The more afraid immigrants are, the easier it is for employers to take advantage of them. And it’s hard for you to compete in the job market against people who have no choice except to accept whatever terms their employer offers.
EDIT: Some people are die-hard racists. Nothing you say will change their minds. But a lot more people have been directly affected by wage suppression. The only people listening to their concerns about the things that directly impact their livelihood are populists who are deflecting blame towards immigrants. If you tell them ‘don’t worry, immigration is great for the economy’ they don’t care. The economy is an abstract concept that doesn’t resonate. If you say ‘immigration is a human right’ then you have the same problem: it’s not a right that the people you’re talking to expect to ever exercise and a right that only other people exercise feels like a privilege. Both messages come across as tone deaf. You are ignoring the problems that they are experiencing and telling them that the downsides for them matter less than the positive aspects for other people. And you’re saying that to a load of people who are right on the edge of the poverty line.
The end state you may want is that national borders are a purely historical curiosity and that free movement everywhere is a universal right. You don’t get to that by alienating a large proportion of voters, you get there by showing those voters that your ideal world is good for them.
The right has shown repeatedly that you can nudge the centre slightly in the direction you want and, after a while, positions that would have seemed extreme are mainstream. The left used to know that. Most of Attlee’s policies would have been far-left extreme policies a couple of decades earlier but the labour movement gradually normalised them.
Your goal isn’t to get everyone to agree with you immediately, it’s to nudge the consensus view towards your position. The approach of ‘moving to the centre’ has just moved the centre away from where you want it to be. You need to frame arguments that move the centre towards you, which resonate with the people that you’re trying to reach. When you split the world into ideologically pure people and everyone else, you discover that ‘everyone else’ keeps winning elections.
EDIT 2: I’m writing this because polling suggests that, in my country, Reform Ltd (a far-right kleptocratic company masquerading as a political party) is on track to win the next election. We have enormous wealth inequality and crumbling public services because decades of kleptocratic governments have looted the public sector. The majority of voters feel this, but the only people acknowledging it are Reform. They are largely the same people responsible for the current problems (not least, those caused by Brexit) but they’re deflecting the blame on immigrants. Their solutions are outright lies.
How is our Labour (a party that spun out from the Labour movement that is now more accurately named Capital, and isn’t even very competent at even that in their latest iteration) government responding? By agreeing that immigrants are the problem (which loses votes from people who know that this is a lie) and promoting watered-down Reform policies (which also don’t make people switch from Reform).
The Green Party (our actual left-of-centre party, which finally won more than one MP in the last election) has a good message on the social side. They point to how immigrants enrich our communities (which should be an easy sell in a country that literally voted ‘Chicken Tika Massala’ as the national dish back in the early ‘90s when we had a Tory government). But on the economic side, they fall back on ‘and they’re good for the economy’. And we’ve had decades of politicians doing things ‘for the economy’ that raise GDP, raise share prices, and just happen to have a negative impact on the most vulnerable.