No, I've never met anyone who is anti-immigration entirely either. They're anti-immigration from anywhere except Western Europe but use language to obfuscate that position.
There's nothing wrong with H1-B visas. As a national position, we should actually be happy that working in the U.S. comes with an economic premium. That's before getting into whether or not American companies are actually paying less for those employees. The H1-b visa is only allowed for 6 years (two 3 year terms). At the end of that time, the individual has to get sponsored for a green card or go home.
In the high end fields, it's far more expensive to invest significantly into staff that you know you're going to lose in 6 years time. That's before factoring in the legal and administrative costs associated with sponsoring these employees. So, while they might make less in their paychecks, a decent portion of that is offset by the investment that the company has to make in these hires.
And since the h1-B situation has always been a capped number, there has never been a "floodgate" situation in effect. At 65,000 per year spread across multiple industries, they're not a large enough portion of the workforce to significantly impact wages across the country, except as a normal effect of excess supply. And for the nation, an excess supply of high end labor is not a real problem. Except for those people who don't like labor competition.
All of those arguments are misrepresentation of how the process works and have found their way in general talking points by playing on some nativist fears about immigrants....because it has very little to do with actual work conditions.