We take your privacy. Seriously.
"We take your privacy seriously" doesn't mean anything but just an expression.
Related article: Stop saying, ‘We take your privacy and security seriously’ by Zack Whittaker
It all really means:
"We take your privacy. Seriously. We don't need to say we are collecting more information from you than we can function as a business. We didn't say it will remain private. I'm sure you know by now. We are ready to say sorry when things go bad because we are not that stupid."