Is it safe to run antivirus software on my database servers?
For me, personally, I have not found it practical. But for 15+ years I have worked in environments that were dedicated to isolating and protecting the database servers. All of the activity that can lead to virus and malware infestation on a SQL Server machine can be prevented IMHO. Extremely limited access, no browsing from the server, no hosting of file shares, rigorous firewall protection, principle of least privilege, etc. Some of these lines get blurred a bit depending on the functionality of your server, for example filestream/filetable.

In my experience anti-virus is often a false security blanket. It is either responding as a post-mortem correction or, in some cases, doesn't have the signature yet for the new threat - either because it is not kept up to date by the system administrator or by the vendor (or both). Since rules and exceptions can change over time, if sysadmins can't keep anti-virus signatures up to date, how will they keep the rules and exceptions up to date?

Your goal should be to secure SQL Server so that you aren't concerned about anti-virus. If you're not having sex, you don't need to buy condoms. :-)