No, it isn't. Republican talking points don't matter, they'll just come up with new talking points, because they're all bullshit anyway. They've brazenly violated the law and are rounding people up off the streets, now is the time to play hardball and refuse to cooperate. The republicans are currently fighting to avoid giving people SNAP benefits, let them, and let's see how that strategy plays out for them at the ballot box.
In terms of optics, what's important is to demonstrate that what the Republicans are doing isn't normal and to make sure there's actual daylight between their positions and those of the Democrats. Caving to their demands will only normalize what they're doing and cause people to give up on going out to vote altogether.
I swear, it doesn't seem to matter to centrists how many times their electoral strategies are proven wrong in practice, because this whole, "move to the right to attract swing voters" is just accepted dogmatically. If that nonsense worked, Trump would never have gotten elected either time.