Hi Taavi,
As the documentation states: it is difficult to use captured external form for subscription center functionality.
https://docs.microsoft.com/en-us/dynamics365/marketing/embed-forms

We know that a subscription center form has multiple checkboxes and they will be mapped to different marketing lists.
However, currently form scanner is only able to map fields of external form to fields of contact entity.
Therefore, if you want to host marketing form on your own CMS, please switch to embedded form instead.
1. Authenticate your domain in Settings > Advanced settings > Marketing settings > Authenticated domains.
2. Create a subscription center type form, after going live it, create a new form page record in Form hosting tab.
3. In the new form page record, copy the automatically generated script.
4. Paste the script to page of your CMS.
5. Create a new content settings record, set Subscription center field to the URL of external page.
6. Before going live a new customer journey, set Content settings field(in General tab) to the new custom content settings.
Then contacts will be navigated to your own subscription center page after they clicking the subscription link in email.
In addition, you could set the custom content settings to the default in Settings > Advanced settings > Marketing settings > Default marketing settings > Marketing email tab.
Please refer to following article for detail about how to set up subscription center:
https://docs.microsoft.com/en-us/dynamics365/marketing/set-up-subscription-center
Regards,
Clofly