UPDATE:
They resolved the problem with my gift card. But the resolution was rather specific to the facts and circumstances of my case, and what they did may not work, or may not happen, for other people experiencing gift card failures.
To understand what they did, you need to understand what I did, and the exact sequence of events.
First, on March 15, I bought a $30 gift card for my 81-year old father. I put it in a drawer until his birthday. He has never used Spotify, and he did not have an account.
Then, on April 13, I helped him create a new account. This was a free Spotify account. Immediately after we set up the account, we tried to add the gift card at www.spotify.com/redeem. And it failed with a generic error message: "Oops, something went wrong. Try again or get help."
After extensive messaging on Twitter, @SpotifyCares failed to resolve the problem. I was asked to try it again in 24 hours. It failed again. I was asked to try it again in seven days. That was ridiculous. Exasperated, and wanting my dad to have the ad-free premium experience, I activated a 30-day premium trial on his account using a credit card. Because it was a trial, the card was not actually charged. The trial began on 04/15 and the card was set to be charged on 05/15. It was at this point that the account became a Premium with Hulu account, even though we never activated Hulu or accepted the terms. In the account panel, the account type was Premium with Hulu.
Even after waiting another seven days, the gift card continued to fail with the same error message.
Today, after extensive messaging on Twitter, the rep suggested that he could fully cancel the Premium with Hulu trial, reverting the account to a free account, and that the gift card would then work. I was skeptical. But I agreed. Keep in mind that the credit card had not actually been charged yet. And he did not simply cancel the auto-renewal. He did an early termination of the 30-day free trial, meaning that we lost the remaining time on the free trial (from now until 05/15). The rep promised to add an additional month to make up for this after the issue was resolved.
And this did indeed fix the problem. After the account reverted to free, the gift card code finally worked. And the rep did indeed add another month. So the account is now paid up until 09/02/19. It is in fact a "standard" Premium account, without Hulu, and there is no credit card on file for autorenewal.
The takeaway is this:
Allowing your account to expire and revert to a free account may resolve this issue and allow you to redeem a gift card.
You can escalate the issue through Twitter and ask them to do an early termination and convert your account to free right now, and that may allow you to add the gift card immediately. But you'll lose any time you have already paid for. Whether they will credit you for this by adding more time on the back end is probably going to be a case-by-case decision.
You may have to just wait for the account expire into a free account. To achieve that, you will have to cancel your subscription autorenewal. And hopefully you can add the gift card the day after the current subscription ends.