I don't think Rex Tillerson is really the problem. In my view, during his hearings, he was trying to be diplomatic by not contradicting Trump's views.
The problem is Trump. He dictates the direction. All arguments between his diametrically opposed team members will be resolved with the exercise of his judgement. He seems to prefer Russia over Germany, and Putin over Merkel. I don't like many of the things Merkel has done in Europe, as you know, but come on. Putin murders his political and media opponents, at home and abroad, and bullies and invades neighbouring countries. These are not equivalents.
Incredible.
At the same time, the argument that many members of NATO are freeloaders is true. It frustrated Obama. But seeming to be a Russian puppet is not going to make folks think they want to engage with the US under Trump. Instead, it's going to encourage the development of a European army. Militarily, you work with those you trust. And Trump just isn't the trustworthy type.