The phrase "that are" is always incorrect because "that" is singular and "are" is plural. The choice, then, is between "that is" and "these are."

The underlying question is whether multiple things ("menus") can 'look like' (or be contained within) one thing. The answer to this question is yes. To make this possibility seem more natural, we must fill in the missing information, that is, supplement the pronoun "that" with that to which it actually refers (or to which it might plausibly refer). For example, consider the following sentence:

That series of images shows what my menus look like.

In this case, "series" is singular, even though it encapsulates multiple items as a single set. This is the basic logic of the first part of the sentence in question.

The problem with the second part of the sentence is that the sentence as a whole is trying to do too much for a single sentence. In reality, all the speaker can demonstrate is:

This is what my menus looked like two days ago.

But, I assume the speaker actually wants to say more than this, specifically something like: This is basically what my menus look like (currently). (But,) these images are a couple of days old. They don't look exactly like this. But, generally this is what they look like.

Or, consider:

A couple of days ago, my menus looked like this. They are still basically the same.

Fundamentally, there are two thoughts here. Therefore, the one sentence is fundamentally flawed. There are any number of "fixes" for remediating the grammatical problem, but all of them (unfortunately) require a higher degree of editorial intrusion than a "minimalist correction" of word, syntax, or punctuation error.