You're over-indexing on the influence of "Fox News and Mark Levin". Most people aren't news junkies. The whole contention is that people who aren't going out of their way to find uncharitable interpretations of "no human is illegal" will think that it's a pro-immigration message. By that I don't mean something like "we should use better names", I mean policies like unlimited migration, or even something like amnesty for all undocumented immigrants in the US. You reject this premise[1][2], but haven't really provided any justification for why that interpretation is unreasonable.
[1] https://news.ycombinator.com/item?id=43973117.
[2] https://news.ycombinator.com/item?id=43973295
>Show me something actually equivalent, and you'll have a point. Find me the most-influential think tank you can that supports stuff like "abolishing the police force" or "denying the basic right for country to have an immigration policy".
>It's correct to say it's a problem for democrats that people think they hold these positions. It's incorrect to say it's because they in-fact do. It's because of effective propaganda.
>You folks are assigning a caricature of their positions to them and then blaming them for adopting those caricatured positions. WT literal F.
Again, my contention isn't that the Democratic party or left-leaning think tanks hold those positions, it's that they're poorly worded, leading independents and centrist Republicans to misinterpret their message, and pushing them away from the Democrats.
Note the original comment you replied to claims that "those kind of positions are a notable and visible part of progressive/Democratic culture". It says nothing about whether such positions are the official policies of the Democratic party.