InDesign: fix wrapping for vertically centered text

Question

See the following screenshot of my current document:

As you can see, there's a graphic frame in the top right that has text wrap enabled. The text in the text box follows that nicely (as you can see in the headline).

Still, even the centered text in the paragraph below the headline is wrapped, although they are short enough. That way, the text looks odd with the second centered paragraph below, since they are not aligned to the same center.

Is there a way to have centered text ignore the text wrap, unless it is absolutely neccessary (e.g. the lines get too long)?

Answer 1

On Indesign the text wrap is applied to objects, but "accept" or not this text wrap depends on the text box.

Selecting this text box > Menu Object > Text Frame Options > Ignore text wrap

Answer 2

Is there a way to have centered text ignore the text wrap, unless it is absolutely neccessary

That's the tricky and interesting part...

Question is: do you really want to wrap overlong text?
Meaning that you would end up with a non-centered line like this:

Imho, it does look a little bit strange, and if I had to do it, I would prefer to have everything centered.

So, I suggest to create an empty frame that would wrap text and place it on the left, like this:

You can see line 2 breaks nicely and stay centered.
Note that I had to place the title in a separate text frame with "ignore text wrap" ON, which also allows you to put paragraph rule under the coffee cup. No more gap due to text wrap: it looks better.

Additionally, you could use content collector to link the the empty frame to the coffee cup. Set up the links options in order to be able to remove the frame content without throwing an update warning.
Then, if you resize your coffee cup, the ghost frame will also resize while updating links. See example below:

Hope that helps ^^