Ive always wondered the same questions but from a somewhat perspective. I'm not a pagan in the Eeuropean sense of the term but more African oriented.
Regardless, though,
How do pagans take seriously what belongs to such ancient cultures that had such different values then we do today?
Pretend that you have a family (if you dont) and you are maybe 80 years old. You have built values, norms, behaviors (cultural traditions) within your family that you do not want to die out. Now you are part of a full community of people that share similar values with their own given norms depending on their location within the country. Regardless, the key is shared norms, traditions, and the need to pass on those practices from one generation to the next.
So your children grow old, their children, and their childrens children. But you are not alone as a family. You are part of a community. Communities branch out and regardless the time period, the motiation and goals are the same as well as the values that shape and change as generations go on until today.
So, Eueropeans today depending on where they are, are still part of a family line of traditions that IS a part of them even if they did not grow up when those traditions begin. (Even if your great great great great great grandchild was born in Hawaii and practice religions in her home country, she is still part of your blood.
So, like other pagans (as she would be considered if she did this) pagans take up and learn about cultures and values that they feel by heirtage they are connected to. It gives us (I will say) a sense of grounding and foundationt o not only know the present-which is important too. Not to yearn for the future since we dont know but to Know where we came from as well.
Its like you are saying to focus on painting a building without acknowledging who built it and who made the foundation of that building. We are all in a community of people.
So....
Why bother resurrecting a crippled horse? How can it still benefit you if it beyond your modern needs? Why not create your own modern day pantheons and rely on ancient cultures that no longer exists or are relevant? Are these cults not outdated and no longer relevant?
On that note, some pagans learn about their heritage beliefs and values as much as they can and apply it to their lives.
For example, a somewhat uniseral value (new agers like protestants some dont do this but not all), the wisdom and knowledge of our ancestors and family in spirit. This is not an "ancient" tradition but one that has been practiced in many forms throughout more than thousands of centuries.
Learning about ones geneology in regards to say where one is from helps a pagan not to reconstruct old ways but to continue the generations of practices even little by little so they go on.
Its benefitial because there are no such thing as Old traditions. Traditions and practices grow and are shaped by the next generation based on where they are and their environment. So thousands of years ago, pagan X may have honored his ancestor by doing one thing while today, the person of same blood and culture may do the same by taking a cigarette lighter to lit a candle instead.
Modern paganism is different but I wouldnt say its modern just its former practiced shaped by the present. All religions go through this from christianity and hindu to, I dontk now Zulu and Lukumi.
The more I see pagans the more I noticed that they alter the cults or syncretize the pantheons to such an extent it bares little resemblance to the practice.
Because there is a huge gap of our parents and our culture given we are great-great-great-greats+ like contrary to popular belief, I find it very difficult to assume the catholicism practiced today has any resemblance to what jesus and his disciples did back when. So its a normal gap. Nothing wrong with that.
On top of this many deities are no longer valid. Deities like Horus were used to signify the monarchy and divine blessing. Other deities had similar purposes or where used to symbolized other out of date institutes.
This depends on the pagan not the deity. It depends on how that pagan sees the deity and more than likely deities dont die (far as I know, right pagans?) so they cant be invalid.
To relate it to my faith, spirits do not die. Nothing disapears out of thin air. So nothing is obsolete. We use cultures from the past that inrich us in the present and guide us in the future. Not many people see the past as valuale until they reach their mid years going through mid life crisis. Im fortunate to have experiences to make me study and learn this early.
Many pagans dont reinvent pagan traditions just try to keep them going without letting them die out. Reconstruction is a poor word for it but it depends on the pagan.