In Finland it currently has to do with the ratification of the Indigenous and Tribal Peoples Convention and other related matters. The Sámi have their own parliament (Sámediggi) that is potentially gaining in influence and so some non-Sámi living in the region supported by certain political parties want a piece of that cake too.I’ve never heard of Forest Sami being controversial before, or any of these claims. Not necessarily saying it’s all wrong, but where did you learn this from?
The Sámi parliament has determined that anyone who speaks or at least whose one grandparent spoke the Sámi language in any of its dialects counts as Sámi, as does anyone whose one ancestor appears as Sámi in public records after 1875. These so-called "Forest Sámi" consist almost exclusively of people that do not meet any of these criteria, yet still want to be a part of the Sámi autonomy. Besides fairly nefarious political motives there are those that have or want to believe they have more distant Sámi roots and find it appealing as a lifestyle choice. Some Sámi are quite irritated also by these attempts to emulate their customs given that even the most sincere "Forest Sámi" generally do not have many surviving family traditions of their own.