In July 2017, I visited 21 UNESCO World Heritage Sites and many museums in Portugal and Northwest Spain (the Autonomous Communities of Galicia, Asturias, Castille-Leon, Cantabria, Basque Country, Navarre and La Rioja).
In both Portugal and Spain, I discovered that there is no free entry for ICOMOS members to any church-run properties I visited, whether they are UNESCO WHS or not. This includes the WHS of the cathedrals/monasteries of Tomar, Batalha, Alcobaca, Evora and Porto (Evora and Porto being part of the Evora and Porto Historical Centres WHSs) in Portugal and of Burgos, Yuso and Suso of San Millan in Spain, and the non-WHS cathedrals of Astorga and Leon. The cathedral of Santiago de Compostela (WHS) is free for everybody.
In Lisbon and nearby Sintra, it does seem that most of the state-run monuments and museums are free-entry for ICOMOS. However, you have to queue at every property to get the free tickets. ICOMOS members cannot order these tickets online in advance, or get joint tickets for multiple properties (e.g., for the museums and monuments of Belem and the palaces and monuments of Sintra), which are available for paying visitors. Queues at these tier one tourist attractions are legendary. Given the shortage in time, I had no choice but to purchase some of these joint tickets in advance and so did not enjoy membership advantages.
The monumental fortresses of Elvas and Coimbra University (both WHS) in Portugal are free entry for ICOMOS members.
In Spain, the record is erratic, and I suspect, often depends on the regional and local governments running the properties. I think those run by the governments of Galicia, Castile-Leon, Cantabria and Basque Country are free for ICOMOS. Examples include WHS such as the Tower of Hercules, Las Medulas and Altamira Caves, and non-WHS such as the Museum of the Galician People and various Basque historical and cultural museums in Guernica.