Probably fake, although there are certainly many true examples of them encouraging mass immigration to western nations, to include a non stop deluge of media propaganda and lobbying pressure on the subject, and censoring and deplatforming people who speak against it.

It's impossible to know the true extent to which they are driving the problem, as they tolerate no scrutiny or discussion of the subject and will aggressively target anyone who seeks to. Basically there is one universal truth in American politics. Nothing of importance happens if there is substantial overall Jewish opposition to it, so if they opposed mass immigration, it wouldnt happen. By contrast the majority of white Americans can oppose it all day long and it wont matter. Trump was an anomaly, and possibly meant to distract from disasterous bush era neocon activities and a passive aggressive attitude towards Israel by Obama, as well as a controlled opposition pressure valve for growing nationalist sentiment in the US.