That protest was probably the one a few months ago against his judicial and constitutional changes, not against this (though there certainly appears to be very real anger against him and his ilk that largely goes unreported here).
As for Putin, I’d have a lot more agreement with him if he hadn’t made a career out of doing exactly what Bibi does - delegitimise opponents, create crises, and then use them to advance his agenda.
If he genuinely wanted to get rid of NATO he could have done it years ago, entirely peacefully and with the blessing of Europe.