Okay with the assumptions from your diagram (vlan4 is your homeLAN) and there is nothing on eth3,4,5
Removed unnecessary stuff…
So at this point, if vlans are talking to each other its because your managed switch is not configured properly.
The firewall rules prevent the router from allowing any user to attempt to reach the other vlan.
The fact that they are in VLANs prevents L2 crosstalk.
I have not seen your bridge rule that includes vlan filtering rule though ------- It is a last step in the config (ensure safe mode button is enabled as for some reason this step can cause the router to burp more than other changes LOL )
/interface bridgeadd admin-mac= auto-mac=no comment=defconf name=1-default-bridge
vlan-filtering=yes
/interface bridge
add admin-mac=XXXXXXX auto-mac=no comment=defconf name=
1-default-bridge ???
/interface ethernet
set [ find default-name=ether1 ] name=ether1-WAN
set [ find default-name=ether2 ] name=ether2-LAN-SWITCH
/interface vlan
add interface=1-default-bridge name=VLAN4 vlan-id=4
add interface=1-default-bridge name=VLAN10 vlan-id=10
add interface=1-default-bridge name=VLAN20 vlan-id=20
/interface list
add comment=defconf name=WAN
add comment=defconf name=LAN
/ip pool
add name=dhcp_pool4 ranges=192.168.4.10-192.168.4.200
add name=dhcp_pool10 ranges=192.168.10.10-192.168.10.100
add name=dhcp_pool20 ranges=10.0.20.2-10.0.20.10
/ip dhcp-server
add address-pool=dhcp_pool4 disabled=no interface=VLAN4 name=dhcp4
add address-pool=dhcp_pool10 disabled=no interface=VLAN10 name=dhcp10
add address-pool=dhcp_pool20 disabled=no interface=VLAN20 name=dhcp20
/interface bridge port
add bridge=1-default-bridge comment=defconf ingress-filtering=yes interface=
ether2-LAN-SWITCH
/interface bridge vlan
add bridge=1-default-bridge tagged=1-default-bridge,ether2-LAN-SWITCH vlan-ids=4,10,20
/interface list member
add interface=VLAN4 list=LAN
add interface=VLAN10 list=LAN
add interface=VLAN20 list=LAN
add comment=defconf interface=ether1-WAN list=WAN
/ip address
add address=192.168.4.1/24 interface=VLAN4 network=192.168.4.0
add address=192.168.10.1/24 interface=VLAN10 network=192.168.10.0
add address=10.0.20.1/24 interface=VLAN20 network=10.0.20.0
/ip dhcp-client
add disabled=no interface=ether1-WAN
/ip dhcp-server network
add address=10.0.20.0/24 dns-server=8.8.8.8,8.8.4.4 gateway=10.0.20.1
add address=192.168.4.0/24 dns-server=192.168.4.2,208.67.222.123 gateway=
192.168.4.1
add address=192.168.10.0/24 dns-server=8.8.8.8,8.8.4.4 gateway=192.168.10.1
/ip dns
set servers=8.8.8.8,8.8.4.4
/ip firewall filter
add action=accept chain=input comment=
“defconf: accept established,related,untracked” connection-state=
established,related,untracked
add action=drop chain=input comment=“defconf: drop invalid” connection-state=
invalid
add action=accept chain=input comment=“defconf: accept ICMP” protocol=icmp
add action=accept chain=input comment=
“defconf: accept to local loopback (for CAPsMAN)” dst-address=127.0.0.1
add action=drop chain=input comment=“defconf: drop all not coming from LAN”
in-interface-list=!LAN
add action=accept chain=forward comment=“defconf: accept in ipsec policy”
ipsec-policy=in,ipsec
add action=accept chain=forward comment=“defconf: accept out ipsec policy”
ipsec-policy=out,ipsec
add action=fasttrack-connection chain=forward comment=“defconf: fasttrack”
connection-state=established,related
add action=accept chain=forward comment=
“defconf: accept established,related, untracked” connection-state=
established,related,untracked
add action=drop chain=forward comment=“defconf: drop invalid”
connection-state=invalid
add action=accept chain=forward comment=“Allow port forwarding”
connection-nat-state=dstnat connection-state=new in-interface-list=WAN
add action=accept chain=forward comment=“Allow internet access”
in-interface-list=LAN out-interface-list=WAN
add action=drop chain=forward comment=“LastRule-Drop all else”
/ip firewall nat
add action=masquerade chain=srcnat comment=“defconf: masquerade”
ipsec-policy=out,none out-interface-list=WAN