Sources:

So, I found a solution that works quite well. Big thanks to avanc and his udev rule that makes this possible. I also modified it so that it could mount up to 4 flash drives at the same time (it can be increased if needed).

Requirements

Install pmount if not installed sudo apt-get install pmount.
This script mounts drives to /media/usb*, so make sure those folders aren't occupied. If you want a cleaner look, don't create any folders.

Udev rule

Create file /etc/udev/rules.d/usbstick.rules
Insert: ACTION=="add", KERNEL=="sd[a-z][0-9]", TAG+="systemd", ENV{SYSTEMD_WANTS}="usbstick-handler@%k"
Save and close.

Systemd service

Create file /lib/systemd/system/[email protected]
Insert:

[Unit]
Description=Mount USB sticks
BindsTo=dev-%i.device
After=dev-%i.device

[Service]
Type=oneshot
RemainAfterExit=yes
ExecStart=/usr/local/bin/automount %I
ExecStop=/usr/bin/pumount /dev/%I

Save and close.

Mount script

Create file /usr/local/bin/automount
Insert:

#!/bin/bash

PART=$1
FS_LABEL=`lsblk -o name,label | grep ${PART} | awk '{print $2}'`

if [ -z ${FS_LABEL} ]
then
    /usr/bin/pmount --umask 000 --noatime -w --sync /dev/${PART} /media/${PART}
else
    /usr/bin/pmount --umask 000 --noatime -w --sync /dev/${PART} /media/${FS_LABEL}_${PART}
fi

Save and close.
Give the permitions sudo chmod +x /usr/local/bin/automount.

Finish

Reboot your RPi and test.

Notes

You can change pmount parameters, but these allow anyone r/w access to usb.
The amount of mountpoints can be changed.
Thanks to avanc for his udev rule and service.

fabricionaweb/Auto mount Raspberry PI USB.md