Anyone have an idea?

Ok. I understand what you are saying. But I don’t know how to check and set the same color spaces on both. When I check color settings (Edit > …), in Indesign and Photoshop these settings are the same.

Or do I have to set something in the output section when exporting a pdf?

I have used a png/psd file before in a Indesign document and never had this issue.

In this example the text layer is on top of everything. It doesn’t make a difference when I rearrange items. Only when I remove the image the text is normal again. Or when I move the background, the text without the background is normal.

Example</img>

Here I have a screenshot of what I mean. As you can see, text without background is normal. With background is bolder and sharper. But only when there is a png/psd on the page.

No, not really. I put text on top of everything, rendering stays the same.