For the moment, I get around this conundrum using a combination of uBlock Origin[0] (Firefox) and NewPipe[1] on Android. Not 100% sure what I'll do about the latter when I switch to iOS.
[0] https://github.com/gorhill/uBlock [1] https://newpipe.schabi.org/
I guess I'm on the opposite side of the spectrum. I want to opt-out of being the product and instead be a customer by paying for "Google Premium" or whatever. It would be an "all things Google" subscription, not just YouTube. Any place there would normally be a Google-curated ad... there wouldn't be one. No more ads at the top of my Google searches. No ads embedded in web pages I visit (rather, Google pays the content provider some fixed amount from my account balance or whatever -- after prompting me to authorize it). No tracking, no "value-add," nothing. Just, "Here's my money, provide me an equitable and reasonable Internet experience that makes sure content providers get fair compensation, and otherwise leave me the fuck alone."
And, most importantly, that would mean that I could never be locked out of my GMail account without a fucking handwritten letter on Crane & Co. stationary with a direct phone number to a human being who I can talk to about whatever is going on.
You could argue that you'd just be paying a gestapo-like figure for the "privilege" of doing stuff that "should be" free. But you're already paying, in the sense that you're the product, and your time and attention is the currency.
Considering that it needs to make actual money (and the streaming royalties for music are kinda expensive).
I find some of the anti-Google arguments to be really, really weird and I've been speaking against Google on this website countless of times.
If you don't want to be tracked, you're going to be tracked for as long as you're a free user. uBlock Origin will not save you, since you're on their website and you can't block "youtube.com".
Also Google is a big target and subject to laws such as GDPR. I actually trust Google more than I trust any startup advertised on HN, because Google is a big target with a lot of eyes watching. When you go to your profile and turn off the data collection, you can probably trust Google more than you can trust DuckDuckGo.
This isn't to say that you should trust Google. Not what I'm saying.
But paying a membership is voting with your wallet against ads. By not paying you're simply encouraging them to serve more ads. And the break you're getting via uBlock Origin is only temporary. If the audience using ad-blockers on Android grows, I expect them to simply block browser access, problem solved. And because you used YouTube anyway, it means you haven't payed for their competition either, which means you directly contributed to YouTube's monopoly, without encouraging them to give up on ads in favor of Premium memberships.
It's basically how software piracy used to work. Piracy was never a problem for the big companies like Microsoft, piracy being responsible in part for Microsoft's monopoly. And when piracy became a problem, software companies simply moved to online subscriptions. There's always a solution for milking free loaders later.
But on firefox you can get play in background with this:
https://addons.mozilla.org/en-US/firefox/addon/video-backgro...
Edit: Firefox on Android. I do not know about iOS
I remember vividly the day (sometime in 2013?) when they removed that feature from the base app. I had been streaming music or casts from YouTube in the background since day 1 of my iPhone 4, and suddenly it became a paid feature.
"Bastards", I thought with a smile, "but hey, fair enough! Ok, now where do I pay?..."
Except that outside of the US, premium wasn't available. So they had removed background play but offered no alternative. It lasted until 2017!! Took them 4 years to bring the premium offer to Europe... what a shame. That fueled some resentment, as a wannabe customer. Any gave more than enough time to find better alternatives (Spotify, youtube-dl...) and never look back.
When they finally introduced premium in my country, I took the free 3 months offer and cancelled immediately thereafter. They don't want my money, 4 years made that emphatically clear.
I may reconsider after 2021, on the condition that management has changed at YouTube and Google. Right now, I'm just not feeling it.
Google is just awful at marketing stuff and customer service. They plain and simple don't care. That's monopoly for us: customers lose, always. So I find it both logical and "the right thing to do" to spend my money to directly support creators and alternative platforms whenever I can.