@Gerben – can you show us the anchor?
All depends where your anchor is positioned…
I have no trouble with text wrap and anchored objects regarding multiculumn text frames.
See the following screen grabs:
Situation 1: Text wrap is active for text AFTER the anchor:
Situation 2: Text wrap is still active for text AFTER the anchor. Unfortunately the anchored object is moved to a position, where text wrap is not possible.
Hope, that helps.
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To expand on that just a bit, there are two "flavors" for anchored objects, inline/above line and custom, and wrap works differently for the two types. For inline/above line wrap affects text follwing the anchor point, but for custom anchored objects wrap only affects text that comes after the entire line in which the anchor is located.
The problem is with what Laubender showed. The left column is texually before the right column where the anchor is, hence the wrap doesn't work for the left column. So you need to anchor early and that means the anchor point itself can end up more easily on a previous page, take the frame with it, which then even more probably ends up before the anchor.
I can understand the difficulty of getting that right computationally in a system like InDesign, you will need to calculate a page and then recalculate because a later object may affect earlier wrap, which will then potentially even move the anchor to a next page. There are solutions, afaik, but it is not simple.
I don't know anyone who uses anchored objects in running text on a regular basis who doesn't encounter at least one problem that needs to be dealt with in some other way to make the layout work correctly. It's just one of those things with the current state of the art.
I used to do stuff like this in TeX. You don't have that problem there with TeX macro packages (like LaTeX and ConTeXt), but on the other hand you have far less control over positioning, let alone wrapping around irregular shapes (possible, but in practice almost undoable).
Doing this gives me another problem. The running view numbers get screwed up. A first unanchored view on page 1 gets number 2, the first anchored view gets number 1, even if it is after a few pages. All the anchored views are numbered before the unanchored ones are.
So, to keep not a too crazy numbering, you need to anchor all objects or have a different naming/numbering scheme for unanchored ones.