No issue in production, just in Beta Cluster.

This might be related to
T62728

This is not anymore Beta-cluster specific issue, I could reproduce it on mw.org today. Will be great if someone could look into it.

By the way. I can not reproduce the problem.

Can reproduce on testwiki.

Can you please explain what you did, to reproduce the problem?
I can not understand the title "Math nodes are not getting rendered for the first time in a login session".
I was thinking that this is a visual editor bug, so I tried to add VisualEditor to the tile, but this edit was reverted.

This is indeed a VisualEditor bug, but it does not occur for first time of each VisualEditor session (which your title was implying) rather on first time after you log in and opened VisualEditor and tried to add a math node.

first time after you log in and opened VisualEditor and tried to add a math node

Do you have any specific settings? It works for me on
http://en.wikipedia.beta.wmflabs.org/w/index.php?title=Math&veaction=edit&redirect=no

At http://en.wikipedia.beta.wmflabs.org/wiki/test?veaction=edit we somehow end up with .mwe-math-fallback-image-inline being a meta element instead of an img?

Nope no special settings. See if this screen capture helps.

"something"😉