The router solicitation and advertisement process which radvd manages requires inbound ICMPv6 to function correctly.
Basically when a host on the LAN boots up it sends out an ICMPv6 multicast packet called a router solicitation asking three questions.
Client: Hello! Who is a router? Should I use stateless auto config or DHCPv6 to acquire an address? Should I use DHCPv6 to acquire name servers and other DHCP options?
Upon receiving this packet radvd responds with an ICMPv6 router advertisement.
Router: Hi there! I am a router, you should use the following preference weight for the entry in your routing table that points to me. You (should || should not) use stateless auto config to acquire an address. You (should || should not) use DHCPv6 to acquire name servers and other DHCP options. Here is the prefix for this LAN for use in stateless auto config.
Since ICMP is stateless I would wager that the RS's sent from your clients are being dropped by iptables and radvd is not receiving them and thus not answering them. Now radvd does send out RA's automatically at regular intervals but that still won't make things work.
This is because in order to actually reach your router your clients must be able to resolve its layer 3 IPv6 address to a MAC address. This process is handled by IPv6 neighbor discovery, which also runs on ICMPv6 using multicast packets. Without going into too much detail, your iptables rules are also blocking these packets and thus preventing the IPv6 functional equivalent of ARP from working. So no L3 -> L2 address resolution, no communication on the LAN.
ICMPv6 also handles path MTU discovery and a host of other things necessary for proper inter-network transit.
So, in short, you need to allow ICMPv6 packets to enter your router (and your clients) for the network to work properly. An IPv6 LAN simply cannot function with ICMPv6 filtered in the way that we are used to filtering it in IPv4. I have seen recommendations to rate limit ICMPv6 but that leaves you open to a pretty trivial DOS attack method so I'm not sure how good of an idea that really is.