You have to do the following first:
On pfsense (in your screenshot LAN) is always VLAN1 and untagged
On pfsense all additional VLANS (in your screenshot VLAN19 and VLAN20) is always tagged
So what you have to do on the HP switch is:
Use one port which is:
TAGGED for VLAN19 and VLAN20
UNtagged for VLAN1 (which is your LAN)
Then connect this port with your pfsense.
This is what you have to do at least. Without that there will never be a correct connection between pfsense and the switch.
If you really want to use dynamic VLANs then you need something which tells the switch in which VLAN the switch should move the computer/MAC-Address. There are probably two possibilities:
an external RADIUS server like freeradius (package for pfsense) or Windows RADIUS Server or any other external RADIUS server
GVRP which will be probably configured on your switch itself
You should search for 802.1X and dynamic VLAN assignment.