You don't know that anything being sold as antique on a site like Etsy or Ebay is either what it says it is nor antique; those sites do essentially nothing to check the reliability of their vendors.

If these items are authentic there's no provenance given (and no 'purchased legally from a private collector' is not a meaningful statement of provenance) and the legality of both the sale and export of such items is of dubious legality. With some exceptions, old artifacts can't be exported from a country without a legal permit to do so. That includes Ukraine, which is a party to the a European Cultural Convention of 1954.

This does not mean that such illicit looting and export does not occur; it does, and is particularly a problem in Ukraine where that Etsy seller is based. Metal-detectorists illegally dig stuff up and sell it online in complete disregard for any laws or ethics and sell it to the ignorant online. It's leading to the wholesale destruction of archaeological sites in some places and these items are forever lost to archaeology because once removed from the their archaeological context (read:. spot in he ground) most of their value to science and history is lost. Even the authenticity may be difficult to retroactively ascertain.

These were probably not found by archaeologists (if found at all, which I hope they weren't) and if they were, there's no reason to believe a looter would necessarily have the expertise to correctly identify objects, and no motive to do so correctly anyway; if they can get more money or more easily sell something by falsely casting it as some 'viking' stuff and sell it to the /r/Norse crows then they're hardly going to be stopped by ethics. (and they do seem to aim fro that crowd what with the big 'VIKINGS' on the seller's main page, and the archetypal use of Elder Futhark runes as some sort of viking logo despite those not being used in the Viking Age)