It's a WordPress site. In the admin dashboard under "Settings" ⇒ "Reading" there's a checkbox, "☐ Discourage search engines from indexing this site." If you check it ("☒") then that inserts the "noindex" directive into the HTML headers and may also do something with the "robots.txt" file.

Given that it was correct earlier, then incorrect, either his WordPress person was really incompetent, or it was done on purpose just so he could claim persecution from Google.

<meta name="robots" content="noindex, nofollow, max-image-preview:large">

The immediately preceding Internet Wayback Machine archive is from July 18, and line 28 there reads:

<meta name="robots" content="max-image-preview:large">

As you can see, both the "noindex" and "nofollow" directives to the "robots" (search engines including, but not limited to, Google) <meta ...> tag appeared some time between July 18 and August 1, asking the search engines to neither index it nor follow links found in it. This is what the "Settings:⇒ "Reading" ⇒ "Ⅲ Discourage search engines from indexing this site" setting does when checked.

Now why would it be unchecked as of July 18, but checked as of August 1? Look at the actual home pages: while the site theme was still the Astra theme (a very popular and configurable WordPress theme [you can tell this by looking at the source code and searching for "/themes" ― the next subfolder in the path is "/astra" so that's the theme directory), there was substantial reconfiguration done on the Astra theme (probably using the WordPress Customizer) including its settings and CSS so that the appearance and layout of the site changed drastically some time between those two dates.

Here's July 18, without the noindex and nofollow (actually I screen-capped July 1 by mistake, but it's the same):


And here's August 1, with the noindex and nofollow:

(Both of these screenshots are 850×1500 pixels, which I believe is Fark's maximum size before resizing. I set my browser to that size before capturing them.)

As you can see, the basic layout is the same: header with petition banners, logo below that, DONATE buttons and mobile menu below that (if I set the screen wider, you'd see full menus), a big banner photo, etc., but the color for the top header is different, and the header photo is different, and other layout stuff you'd see further down the page is different. In other words, a substantial redesign.

It's pretty obvious what happened: some time between those two dates, the graphics people in his campaign felt that a redesign was needed, so they got the WordPress person to do some reconfiguration. But since they didn't want people to see the "pardon our dust while we remodel" type thing going on, they first made a copy of the site into a staging directory on a subdomain (or perhaps subdirectory) URL that they could easily get to but that the general public wouldn't know (say, "testsite,votefinchem.com"), and to keep that from being exposed to the public, they went to "Settings" ⇒ "Reading" and checked the "Settings:⇒ "Reading" ⇒ "Ⅲ Discourage search engines from indexing this site" checkbox, which inserted those two directives into the "robots" meta directive on Line 29.

After the graphics people and likely Finchem himself signed off on the new look, the web server person then pointed the web directory for the main site to where the staging site was, so that there'd be no downtime: the next visitor would suddenly see the new design. But either they forgot to tell the WordPress person to uncheck that checkbox because it'd gone live, or the WordPress person just forgot to do it, so that checkbox remained checked and those directives remained inserted.

So, no, I don't think Finchem's people did this on purpose to give Finchem an excuse to claim that he's being persecuted by Google. That said, he certainly jumped at the chance to do so. Persecution complex is epidemic among especially the Nat-Cs, because Jesus promised them that they'd be persecuted because of Him, so they look for it wherever they can because Jesus couldn't be wrong, now, could He? (See also "Happy Holidays" = "War On Christmas.")