Is "Winston tastes good like a cigarette should" still considered ungrammatical?

I think it has become more acceptable to use like where many writers might once have used only as. In his book The Careful Writer (copyright 1965), Theodore Bernstein has an entertaining entry for Like/As (page 258) that includes this:

Shorts are not acceptable dinner attire in most better-grade restaurants. There is no really logical reason for that, although restaurants could advance other kinds of reasons. But it takes a daring soul to defy the proscription. Similarly, the use of like as a conjunction ("In an experimental water tank, quartz crystals beamed sound like floodlights beam light") is not acceptable in better-grade writing, although there is no logical reason why it should not be.... There is no logical reason why like should not be regarded as a conjunction; on the contrary, there are sound logical and historical reasons why it should be. And yet ... yet ... there are those objections by grammarians. Reasonable or unreasonable, they are a force in the language as it exists, as contrasted perhaps with how it should exist. The force has been exerted through generations of teaching and precept so that the objections are strongly entrenched. That does not mean that they are eternally entrenched. Indeed, there is every sign that the popular usage is finding its way more and more into print in the form of AD-DICTION: "Winston tastes good—like a cigarette should"; "Flattens hills like it flattens the floor." Perrin says (1942 edition): "If editors and publishers did not enforce the use of as instead of like according to the rule in their stylebooks, it is possible that like would become the dominant form, and it increasingly appears in print." The belief is well founded only in part. Not only editors but also most writers have an ingrained distaste for like, and do not merely adhere to a rule in their stylebooks. It will take more than a fiat by an authority on usage or an undiscriminating count of noses to bring about a change. The change is not here yet, and the serious writer who uses like as a conjunction still does so at his peril. Some eminent writers have appeared in the restaurant in shorts, but their eminence has perhaps protected them. The evidence—and it is significant—seems to be that far more eminent writers have avoided appearing in shorts.

Fast-forward nearly 50 years, and you know that Bernstein was right, that the proscription to use like as a conjunction is not eternally entrenched.

In his book The Grammar Bible (copyright 1999), Michael Strumpf writes (p. 272):

In colloquial speech, like is accepted by many as a subordinate conjunction. Language is forever changing, and usage ultimately determines what is right and what is wrong despite the protestations of the purists. Purist though I am, I do not stubbornly resist change, even if it occasionally rankels! The use of like as a conjunction in contemporary English is so widespread that no one can deny that the word has found a new role. Few would argue with the grammar of a sentence such as "It looks like rain," but the sentence contains a subordinate clause introduced by like. The verb has been omitted from the subordinate clause like rain. Even The American Heritage Dictionary acknowledges the legitimacy of using like as a conjunction when the verb has been removed from the subordinate clause. Those who avoid using like as a conjunction across the board will find their sentences to be tortured.

There never was a general principle as to why like could not be used conjunctively, and it is now strongly supported by corpus data from around the English-speaking world.

'The Cambridge Guide to English Usage'