We should be careful in our definitions.
"Celtic" is purely a cultural distinction. Even back in classical and pre-historic times, the Celts were likely not one homogenous tribe but rather various peoples linked by a common culture, common language, common society and religious practices. In other words, they were Celtic because they belonged to a Celtic culture.
There is no Celtic morphological type just as there is no Celtic gene.

The Irish and Spanish are genetically very similar. This does not preclude either from being Celtic though.
Not all of Iberia was Celtic but some of it was, just as Ireland was not always Celtic but became some in time.
Being Celtic doesn't mean a tribe called the Celts came and took possession of the land. It meant that people settled who were Celts because they brought Celtic culture with them. That is what makes a people Celtic.

So yes, being Celtic does link Iberian and Hibernia.
But there is more to it than even that. It goes even further back to beyond Celtic societies (although in fact the Irish Q-Celtic language likely arrived from Iberia as opposed to the P-Celtic of the Britons which was likely related to Gaulish). Personally I am proud of my Celtic heritage. But I realise the links most likely reach back to the first modern humans in Europe. The link is an exceedingly ancient one, which has still not wholly faded but lingers on in an appreciation and respect among each of these ancient peoples for the other.