Given the following example:

<div style="display: grid; grid: 50px / auto; width: min-content; font: 25px/1 Ahem; border: 5px solid;">
   <div style="color: magenta; background: cyan;  writing-mode: vertical-lr;">XX X</div>
   <div style="color: red; background: blue; grid-column: 2;">XX X</div>
</div>

Loading this example in Chrome or Firefox we've got the following results:

Chrome

Firefox

Current draft of Grid Layout specification states the following regarding grid container's intrinsic size computation:

5.2. Sizing Grid Container

The min-content size of a grid container is the sum of the grid container’s track sizes (including gutters) in the appropriate axis, when the grid is sized under a min-content constraint.

In the example defined above, we need to use grid's container intrinsic size as the available space for steps 1 and 2 of the Grid Sizing Algorithm. After executing them, the orthogonal item has changed its min-content contribution, so as it' state in the specs we need to repeat steps 1 and 2 with such new min-content contribution.

Since we are in the middle of a layout, we shouldn't compute again grid's container size, so even though column tracks's size have changed after running step 3, they is not reflected in the grid's intrinsic size.

3- Then, if the min-content contribution of any grid items have changed based on the row sizes calculated in step 2, steps 1 and 2 are repeated with the new min-content contribution and max-content contribution (once only).

Hence, I think we have an issue on how grid's intrinsic size is defined when there are orthogonal grid items; at least, if we really want to apply step 3 of the tracks sizing algorithm. I assume it's clear that we shouldn't make intrinsic size computation to depend on layout.