How to stop "Powered by Admiral" anti ad-block pop-up messages?

I've recently noticed a TON of sites using this Admiral anti-ad-blocking software.

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The site loads normally, then this annoying Admiral pop-up loads a few seconds later.

I won't be disabling my content blocker to read these sites. Sometimes I can click "Continue without disabling", but sometimes that option does not appear.

How can I prevent these pop-ups via a browser extension?

No need for any additional extensions. Within your adblock extension subscribe to one or multiple anti-adblock lists like these Anti-Adblock Killer or EasyList ones, which include Admiral blocking and should be compatible with all the major adblockers. Other various lists can also be found.

I would also recommend running list(s) like that with uBlock Origin, which is the fastest and most reliable one by far. It gets rid of lots of annoying anti-adblock measures with default filters, it also attempts to fix some sites that don't like that. For remaining ones you could enable optional Annoyances type of list(s).

Just note that its support in a Chromium-based browser like Google Chrome might end anytime soon due to Manifest v3. There are e.g. registry workarounds for that though. Or you could try uBlock Origin Lite that has bunch of limitations compared to the original one, but it attempts to work around them.