windows 10 - Is it safe to update to 1903 even if my computer says it's not ready?

From here, I can manually update to 1903: https://www.microsoft.com/en-us/software-download/windows10

However, on the Windows Update screen, I am presented with the following:

Does this mean I should wait to update manually, as well? I would really like the latest version of Windows if possible.

Answer

Does this mean I should wait to update manually, as well?

There is some hardware and/or software currently installed on your system that is not compatible with Windows 10 version 1903 at this time.

I would really like the latest version of Windows if possible.

You will have to wait. The only way you would be able to install 1903 at this time, would be to perform a clean installation, even then that isn't guaranteed to work. Windows Update, Upgrade Assistant, and Media Creation Tool all will present you this same message, which is indicating there is something that blocking the upgrade, all you have to do is simply wait until that hardware and/or software conflict is resolved.

You should absolutely not attempt to install Windows 10 version 1903 at this time.

Ok, will wait (this one is my work comp).

If any user on my network took it upon themselves to install a feature upgrade without permission they would no longer have a job. You should absolutely NOT upgrade the machine in question.

My home computer has no such warning on its Windows Update screen, so I'm taking a shot and seeing if it'll update.

Your home computer has different hardware and software installed. If you are offered the upgrade and do not receive the message you are asking about, then you can proceed to upgrade your own computer.