Since your goal is "to move to a European registrar" Porkbun is not for you.
https://hosting-checker.net/websites/porkbun.com "Webserver Amazon"
Here are some additional options. https://european-alternatives.eu/category/domain-name-registrar
https://1984.hosting/product/hosting/
I suggest you reach out to Infomaniak support and ask for an alternative method which is less invasive.
https://www.infomaniak.com/en/help
Try to make Infomaniak a better experience for everyone. Infomaniak claims to be "The Ethical Cloud" but they did not start business as a privacy company and have been learning over time. Help to teach them with one more customer story. Let us know what happens.
If no luck with Infomaniak helping, you can try to contact a different registrar before signing up to confirm they will accept your domain type and ask them what the process will be. Hold them accountable to whatever process they describe if you choose them.
Thank you for the great work you do! Here is a link with additional options to consider.
https://www.eucloud.tech/eu-alternatives-to/cloudflare
If you are only willing to consider a no-money option, it will be more difficult. Maybe consider approaching an alternative and asking if they will support a non-profit for a discount.
Another option is simply to drop Cloudflare without a replacement. You have raised some of the tradeoffs. Maybe people can live with those tradeoffs.
There is the consideration of Cloudflare tracking users from one domain to another. Pornhub is one site notorious for using Cloudflare.
https://www.ghostery.com/whotracksme/tracking-reach
There is also the consideration of Cloudflare possibly decrypting traffic and compromising passwords. At the start of a possible physical war, disrupting communication by overtaking user accounts could be a possible threat.