Not as rich as they make themselves seem (like)

"These girls on Instagram aren't as rich as they make themselves seem (like)."
"Things aren't always what they seem (like)."

Is 'like' redundant in these sentences? I heard the second sentence from a native speaker.

It's not just redundant; it's wrong, in my opinion.

Things aren't always the way they seem.

The first sentence is definitely wrong. If you rephrase, you can see why:

These girls seem rich.
These girls seem like rich.

The second sentence isn't wrong, though, if what is substituting for a noun phrase rather than an adjective phrase.

• seem + adjective phrase
• seem like + noun phrase
• seem (+ that) + clause