Yes, access ports also send BPDUs (because STP runs on all switch ports by default). So in your scenario, The access port sends BPDUs for the single spanning-tree instance, the trunk port also sends BPDUs for the same instance, the MX doesn’t process them, it just forwards them like normal frames if both ports are in the same bridge domain and the VLAN carrying those BPDUs is allowed on both links. When the switch receives its own BPDU back on the other port, RSTP detects a loop and will block one of the two ports (usually the one with the higher port ID or cost). This is because STP doesn’t care about VLAN separation here, it’s one topology for all VLANs. So the only way STP does not block is if, the access VLAN is not allowed on the trunk, BPDUs never loop back, STP sees no loop, both ports stay forwarding. If the access VLAN is allowed on the trunk, the MX forwards BPDUs, STP sees a loop, blocks one port. If the trunk includes the access VLAN, RSTP will block one port. If the trunk excludes the access VLAN, STP won’t see the loop and both ports will forward (which is risky).
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