Completely false -- many on the "left" complained about both Obama's treatment of immigrants and his handling of drone attacks while he was in office so there was no "silence" on the issue.
There may not have been as much dissent as we see with Trump, but people definitely weren't silent on the "left" about these issues, and they were certainly more outspoken at the time than those on the "right" with regards to Trump's current openly malicious treatment of immigrants. Moreover, "deporter in chief" Obama likewise promoted DACA and a pathway to citizenship in his immigration efforts, while Trump calls immigrants "rapists and criminals" and does his best to treat them as such.
One could even argue that the real hypocrisy is on the "right" in that respect -- illegal immigration dropped sharply under the Obama administration, yet you see people here still trying to claim that Democrats are for "open borders" in a weak effort justify Trump's behavior.
That said, the reason there was less "outrage" over Obama than over Trump is because Trump is intentionally separating children from their families as a deterrent and refusing to provide immigrants with things like soap, toothpaste and basic medical care.
The amount of "outrage" is directly related to the intentional cruelty towards immigrants espoused by both Republicans and the Trump administration -- the more outrageous the action (like intentional cruelty towards children or starting the Iraq War on false pretenses), the more people will respond to it.