It is not
Trump shouldn't make a shopping list and an enemies list too.
but rather:
Trump should not make an enemies list as Nixon did.
Nixon made an enemies list. An enemies list should not be made by Trump, too [i.e. in addition to Nixon, or adding his own name to the names of presidents who made an enemies list].
This is a perfectly idiomatic colloquial English statement. The placement of too can create ambiguities, but context usually clears them up.
The statement means "Trump, now, should not be doing the same thing himself".
Suppose someone asked the same question yesterday, and now today you're asking it. One could say:
This question was asked and answered yesterday. You shouldn't be asking the question too.
P.S. either instead of too there would say that neither Nixon nor Trump should have engaged in the practice. too does not entail anything untoward about Nixon, just as in my last example with too there's no critique of the person who asked the question yesterday.