I use AdBlock Plus on Firefox/Windows and my experience has been the same as Lindy's. I've not encountered any blocking when clicking on Ancestry and/or affiliate links that are on a profile page.
The problem that I've encountered is that when the profile page (or another page, such as the quiz page that was the original topic of this post) is rendered in the web browser, the ad-blocker suppresses links to the ancestry domain from being displayed on the profile, so there's no link present in the profile on which to click. The ad-blocker does not suppress links prefixed with the Ancestry affiliate code, so those links are displayed on the profile page, and I can click on them to successfully reach the intended page. The ad-blocker also does not suppress any Ancestry external link templates in use in the profile, so those links are also displayed on the profile page, and I can click on them to successfully reach the intended page. As Ellen and others have indicated, if I disable the ad-blocker and refresh the profile page, links to the ancestry domain are displayed on the profile, and I can click on them to successfully reach the intended page. But again, that only resolves the issue for me.
As Ellen also stated (and is also my understanding), "affiliate links become part of all Ancestry.com URLs when we click on the URLs". But for the situation that I'm encountering, there is no Ancestry.com URL link on which to click, because links with the Ancestry.com URL are suppressed by the ad-blocker when a profile page is rendered in the browser.
Again, this is what I'm experiencing. Hope this makes sense!