Any ideas why this is happening?
Yes. Windows Server has a service called Network Location Awareness (NLA) that determines what network that computer is connected to a very general sense, sets a Network Profile (Public, Private, Domain) which in turns actives a wide array of default settings.
When the SAN1-4 network cards are enabled, Windows identifies the LAN network as a public network and bang - firewall gets in the way.
This is odd. In Windows 7 / Windows Server 2008 R2 (and presumably Windows 8 / Windows Server 2012) you should be able to have per-interface Network Profiles assigned, thus your LAN interface can be using the Domain profile but your WAN interface using the Public profile. Consequently, I'm not sure why enabling your SAN NICs should change the Network Profile for your LAN NIC. One approach would be to see if you can figure out why you can't have multiple active profiles because as far as I remember you should be able to do this.
On the other hand, you probably just want your LAN NIC to be using the Domain Profile and your SAN NICs to be using the Public Profile (see @joequerty's comments) or even a custom Network Profile with corresponding firewall rules configured.
Here's what has to happen for the Domain Profile to be assigned to an interface:
If the Connection Specific DNS Name matches the
Policy\History\NetworkName” registry key then the machine will attempt
to contact a Domain Controller via LDAP. NLASVC does this by calling
DsGetDcName on the forest root name and issuing an LDAP query on UDP
port 389 to a root Domain Controller. The service expects to be able
to connect to the PDC in the forest domain to populate the following
registry subkey: HKEY_LOCAL_MACHINE\Software\Microsoft\Windows
NT\CurrentVersion\NetworkList\Nla\Cache\IntranetForests. If both these
steps succeed, you will get the Domain profile.
You can just force the default Network Profile assignment for unidentified networks with a GPO:
Computer Configuration->Windows Settings->Security Settings->Network List Manager Policies
See Disable Windows Server Network Locations? for more information.