No, you aren't adapted to the diet your scandinavian ancestors ate and you won't loose the ability to digest those modern foods.
You are partially adapted, though. While salt, dairy and cod are not a problem the adaption to cereals and refined carbs that may have occured is not enough for you. People of scandinavian descent have especially high risks for western diseases like cancer and cardiovascular diseases. They had much less time to adapt to carbohydrate rich cereal foods than people in southern europe for example.
I see no reason that raw milk products are bad when consumed by healthy individuals. We have to evaluate food not only from a evolutionary perspective but also what contemporary science tells us about its biochemistry, nutritional quality and effect on humans.
Cereals are a different story. Not only do we have evidence that they were first introduced in massive quantities only a few thousand years ago, but even science has discovered abundant negative effects on overall health, reporting that grains are involved in nearly every degenerative disease known to mankind.
And no, avoidence of wheat and dairy can you only do good. I don't know if you really mean allergies or just food sensitivies.
People today seem to be sensitive to just everything.
Environmental chemicals, lectins, a weakend immune system, stress, sleep deprivation, nutritional deficiencies, antibiotics in excess, refined sugar, not being breast-fed, candida are but a few factors which lead to greater intestinal permeability.
All those things attack the intestinal lining, making it susceptible for undigested food proteins to go into the body and provoke autoimmune responses.
If you avoid foods which are known to damage the intestine you can heal your leaky gut.
To answer your question, with a healed gut you are even better able to tolerate neolithic foods because it is more unlikely that undigested food molecules enter your blood.
Many people experienced that, after a few years on a carbohydrate restricted paleo diet, they are able again to digest food they were sensitive to. Like dairy, eggs, or even traditional bread.
It is true that we can eat a diet which contains grains, if they are sorougly fermented and the diet is nutrient-reach overall. That's what Weston Price showed us. Degeneration occurs with processed, nutrient-deficient food which isn't prepared to destroy the anti-nutrients. That doesn't mean it's optimal, but at least this is the way to go if we only have those kinds of food available.
But since most people today are exposed to so many "agents of disease", it is necessary to go paleo so that real healing can occure because we are health-wrecks compared to a healthy born Weston Price-style baby.
Personally I believe that not only diet but also modern chemicals and heavy metals, medication, stress, trauma and sleep deprivation combined provoke the diseases which are so common today. But anyway, it can only be good to avoid certain neolithic foods for sometime to heal, you won't loose your ability to digest them. Though you can notice food sensitivies later because your body became more sensitive due to abstinence