Two points here.
Conditional redirection and SEO
The conditional redirection isn't a problem if correctly configured. In Google's case, they're now using "locale aware crawling", whereby their crawler employs different
Accept-Language values (i.e., browser languages) and IP addresses.
That being said, we don't know much about precisely what languages and regions are supported, and their own page on locale aware crawling advises continued use of
Further, other search engines do not, as far as we know, have equivalent features. For them, we should assume they do not issue
Accept-Language headers, and likely crawl from a single location.
When conditionally redirecting, you'll typically have a fall-back redirect. For example, if you have only English and Italian content, a visitor with a browser set to German will go to whatever you decide is the best default.
Taking locale aware crawling out of the equation, that default scenario will apply to search engines. So, to ensure your country/language-specific content is crawled and indexed properly, you need to make sure it's all accessible despite the conditional redirection.
It may be helpful to refer to my answer on a previous, similar question.
Problems with using browser language for conditional redirection
You haven't asked about this, but it's worth pointing out. Browser language can be an unreliable indicator. Most browsers default to US English, and many users either don't know or never bother to change it.
For this reason, if you use your analytics to compare traffic by language and location, you'll often see a discrepancy.
It's usually most visible between variants of English (US, UK, Australia, Canada, etc.). Looking at one of my client's data now, for example, I see that, judging by browser language, they have almost 3 times as many visitors from the US as IP addresses would suggest.
May not be an issue for you, but worth considering.