Ordering of co-primary authors on website
In Can co-first authors’ positions be swapped in a CV?, the answer with the most upvotes says


  No. The reference is the reference, changing it to move yourself higher could be misinterpreted as willful deceit.


I believe the same logic applies to a website.

However, in a website, you do have more freedom in style and formatting than you would in a CV (although you still don't have the freedom to change author order...) For example, if you want to call attention to first authorship, you could list first authors and co-first authors in a slightly different weight or different color than the other authors.