No. Wishpicks doesn't hand your wishlists to Google. A list set to Anyone with the link or Invite only is never indexed by search engines, so it won't turn up in results.

Anyone with the link (the default) isn't indexed, isn't on your profile and isn't browsable. The only way in is a link you shared.

Invite only isn't indexed either, and only you and the people you invite can open it. Everyone else gets a "No Access" page.

Public appears on your public profile, so anyone holding your profile link can reach it from there. It's still not placed in any browse page, feed or search on Wishpicks.

Your public profile lives at a handle like /@yourname, and profile pages are tagged to ask search engines not to list them. Search engines don't always take the hint, though, especially for a page they find linked somewhere else. If you'd rather a list stayed off your profile entirely, set it to Anyone with the link or Invite only.

In practice, what makes a wishlist findable is where the link gets pasted. A forum post, a public social post or a group chat that search engines can read will do it. That part is up to you.

Switching a list from Public to something narrower takes it off your profile straight away. If a search engine already indexed the page, it drops it on its own schedule, which isn't something we control.

There's no single switch to make your whole profile private. You set visibility per wishlist, so you decide list by list.