Back in the old days, search engines mostly crawled your sites with their regular, clearly identifying HTTP User-Agent headers, but once in a while they would switch up to fetching with a browser's User-Agent. What they were trying to detect was if you served one set of content to "Googlebot" but another set of content to "Firefox", and if you did they tended to penalize you; you were supposed to serve the same content to both, not SEO-bait to Googlebot and wall to wall ads to browsers. Googlebot identified itself as a standard courtesy, not so you could handle it differently.
Obviously those days are long over. It's now routine and fully accepted to serve different things to Googlebot and to regular browsers. Generally websites offer Googlebot more access and plain text, and browsers less access (even paywalls) and JavaScript encrusted content (leading to people setting their User-Agent to Googlebot to bypass paywalls). Since people give Googlebot special access, people impersonate it and other well accepted crawlers and other people (like me) block that impersonation.
This is part of an increasingly common general pattern, which is that different HTTP User-Agents get different results for the same URL . Especially, some HTTP User-Agents will get errors, HTTP redirections , or challenge pages, and other User-Agents won't; instead they'll get the real content. What this means in concrete terms is it's increasingly bad to take the results from one HTTP User-Agent and assume they apply for another . This isn't just me and Wandering Thoughts ; for example, if a site has a standard configuration of Anubis , having a User-Agent that includes 'Mozilla' will cause you to get a challenge page instead of the actual page ( cf ).
(One of the amusing effects of this is what it does to 'link previews', which require the website displaying the preview to fetch a copy of the URL from the original site. On the Fediverse, fairly often the link preview I see is just some sort of a challenge page.)
In practice, you're probably reasonably safe if you're doing close variations of what's fundamentally the same distinctive User-Agent. But you're living dangerously if you try this with browser-like User-Agent values, either two different ones or a browser-like User-Agent and a distinctive non-browser one, because those are the ones that are most frequently forged and abused by covert web crawlers and other malware. Everyone who wants to look normal is imitating a browser, which means looking like a browser is a bad idea today .
Unfortunately, however bad an idea it is, people seem to keep trying fetches with multiple User-Agent header values and then taking a result from one User-Agent and using it in the context of another. Especially, feed reader companies seem to do it, first Feedly and now Inoreader .