Is it ok to ask others to shop for you when they are travelling?

Good post. As an expat I also get asked to bring things to Sweden. Beer for example. Chocolate. My answer is exclusively no. Would I go by car, maybe something but plane, never. Carrying bottles from duty free also never. Too heavy.
And no, I don't ask people travelling to bring me things either, unless they offer themselves and then it's all about cigarettes for me.
Friends and family who come here usually ask if they should bring something. There will be 3 things isf; snuff, cheeses and a weekly magazine with crosswords.

I am like you and shop at home most of the time (except for some unusual English gin that would be very expensive to import privately but I have bought it on the spot and not at duty free). I don't buy for others either but friends know that I travel by train most of the time. If I ask for something myself, it is mostly small things from colleagues going to my old home countries. A box of favourite chocolates from Brussels or crumpets from the Brit who is going to England and will be visiting a supermarket (the few sold here are from a Brexit company I boycott).

For a start, tax-free shopping is not the same as it was some 20 years ago. This applies to both airports and Finnish cruises. Back then, it paid to shop tax-free, which is no longer the case.
In the past I would ask acquaintances travelling abroad who I knew did NOT smoke to buy me a loaf of bread, which they were happy to do. I have never asked anyone to buy me wine/spirits, as they obviously buy for themselves.
If you want to buy "cheap" wine/spirits and tobacco, it is often more favourable to do so in supermarkets, as prices are lower than in so-called tax-free places.

I think it depends. Who you ask, what you ask about, what context. Personally, I usually only ask close family. Acquaintances are more exceptional cases, for example if it's about something very important.

Then I think that whatever you ask for should not be available at home, or be easy to order. It should not be about saving a few kroner on buying something in duty free that has to be dragged with / home. Instead, what you ask for should be something special that can only be obtained in a specific place.

I have shopped for others, and have asked others to shop for me. Sometimes it's something simple from a supermarket, sometimes something that requires more time and commitment from the traveller. But it should always be on the traveller's terms and I don't think you have the right to be angry if you don't get what you "ordered", regardless of the reason why it didn't arrive. Sure, you can be disappointed, but then maybe you can try to keep it to yourself so as not to give the traveller a bad conscience.

The only person I shop duty free for is my partner when I've travelled alone, and even then there's no guarantee he'll get what he wants. Sometimes I can't carry anything heavy, sometimes there's no room in my bag, and sometimes I haven't had the energy to run around the airport at all.

It is very difficult to make everyone else happy and satisfied, but in the end it is most important that you are happy and satisfied. Of course it is sad to give sad news that you did not have time for their wishes, but in the end I think you should see it as just that; a wish. Shopping for someone else on their own trip should not feel like a requirement.

Wow, I hadn't realised that it's rude to ask someone to bring something. I live in Crete and often ask friends and acquaintances to bring me things... Not as often as before but still. Many friends who have dragged on rag rugs, gruel, fish balls, sweets and anchovies. But often they come down with a lot of space left in the suitcase. Those who travel with only hand luggage, I of course do not ask and should there ever be someone who finds it difficult to bring something, I of course accept and understand it, but most people I know actually ask if I have any "wish list" before they come.