Multi Filter doesn't communicate with the colvis function

Hi all,

with the help of the community I was able to put a multi filter search in the head of a table. But with using the colvis function, this filter doesn't communicate with the columns. As you see in the example they indeed reduce from e.g. four to three columns, but the search function doesn't go with the colvis function. The function stays in the original column.
https://jsfiddle.net/RoloTomasi/vhp3fjxd/6/
Any ideas?

Thanks in advance
Rolo