It’s not possible to mount a share as „User X“ ?

Geht nicht. Gibts nicht.

bindfs is the answer.

It will take an already mounted file system and provide a view of it with whichever uid you’d like:

sudo apt-get install bindfs; # install bindfs
mkdir /mnt/mointpoint; # make mountpoint where to mount
sudo bindfs -u $(id -u) -g $(id -g) /media/source /mnt/mointpoint

now you will ask: What is my USERID/GROUPID?

id -u; # display user id of current user
id -g; # display group id of current user

# alternative:
cat /etc/passwd|grep user