I disable auto-update and get my software from a computer not associated with me. I compare checksums to copies that friends have and checksums on virustotal.
For linux software, I validate GPG checks of individual packages and of the rpm repo. Both packages and metadata are signed. I get the public key from a non mirror site and compare to keys listed by others.
This does not preclude back-doors, but it means that everyone has the same backdoor as me. I then mitigate dial-home of said programs with firewall rules and selinux. If there is a hard-coded key, it will also affect all the companies and governments using the same software.