Should I warn a professor about his bad internet security practice? A relatively old professor from another institute "forwarded" to me, using his work email, a work-related message he had received on his Gmail account.

However, he actually saved the entire Gmail webpage and attached it. A saved Gmail webpage may contain personal information and should not be shared with others.

He is based in a distant city and I didn't meet him in person (yet), but we work remotely on the same project.

Should I care and tell him about this bad security practice? How?
If this was a one-time thing and you don't know this person very well, I would avoid bringing it up.

Once you know this person fairly well or communicate with them on a semi-regular basis, then sure, in your next email to the person just put as a note at the end of the email that they might be cautious about including the entire webpage.

The concern is that it might be off-putting to someone if they don't know you well and perhaps this professor actually verified that no personal info was included.