One on my clients want me to host an adult website.
Will it affect my other websites on the shared server or should I get a separated server?
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If you do not have specific experience running this kind of websites, then I would strongly suggest you to get a separate server. While having an adult site on same server with different websites might not affect your non-adult sites directly, there are plenty of things that can go wrong (e.g. IP flagged/blacklisted for "spam"-like emails, content IP-blocked due to inappropriate content in some countries) which will affect other websites.
Do you mean with regards to search? From Google's point of view: no, that's fine. There are a limited number of IP addresses, so you need to share.
The only exception I can think of is if you have a ton of really spammy sites on a server, and just a tiny number of good ones, but that doesn't sound like your situation. In cases like that, we / our algorithms may have a hard time taking the appropriate granular action on those spammy sites, and may choose to take action on the whole server instead. These situations are really rare though, and if you're using a normal web-hoster that cares about what's hosted on their servers, that's not something you'd run into. Also, "adult" doesn't necessarily mean that it's spammy.