Perhaps the novels of the Brontë sisters would qualify. Reviews were often mixed, always recognizing how popular and enjoyable the stories were, but often deploring the subject matter. Also, as novels concerned with women and particularly beloved by women, they were considered to be in a lesser category, like children's literature.

I think Wuthering Heights, by Charlotte Emily Brontë, was probably the most controversial. Here you can read some contemporary reviews where the writers simply did not know what to make of it. An example:

Wuthering Heights is a strange, inartistic story. There are evidences in every chapter of a sort of rugged power—an unconscious strength—which the possessor seems never to think of turning to the best advantage. The general effect is inexpressibly painful. We know nothing in the whole range of our fictitious literature which presents such shocking pictures of the worst forms of humanity.

There have certainly been books that were considered critical and commercial failures that ended up as great literature. As the other comment notes, the answer to your question depends on what you regard as "trashy."

As an example of a book that originally failed, Moby Dick provides a very good sample. While originally published in 1851 in America and England, it was not until the early twentieth century that it became well admired. When it was originally published, reviews were decidedly mixed, but more telling was the public perception of the novel. While initially mixed like the critical reception, the public perception worsened as Melville published other unpopular works such as Pierre: or the Ambiguities.

Eventually the reception became that these works, including Moby Dick, were monstrosities and mistakes. While it had a handful of admirers in England and Scotland, it became virtually nonexistent in America. In fact, the year it was released, only 2,000 copies were said to have been printed, while books like Uncle Tom's Cabin printed in the hundreds of thousands.

This was until the early twentieth century when, what could be termed a modernist revolution, began to appreciate the stylistic approached found in works like Moby Dick. Sadly, Herman Melville passed away in 1891, long before Moby Dick ever received its praise.

Source: New Essays on Moby Dick by Richard H. Brodhead

I don't know if this is necessarily an answer to the question you were asking, as the responses for Moby Dick were not negative due to promiscuity or anything of that nature. Perhaps it would be useful if you defined exactly what you meant by "trashy." I think it would be relevant to define who found the novel "trashy". If you are referring to religious groups, the list is likely extensive (I can think of The Scarlet Letter as an example just off the top of my head). If you are referring to the general public or critical reception, the question becomes a bit trickier.

My understanding is that most of William Shakespeare's plays were intended to be "trashy" pieces for the enjoyment of lower classes. Consider the opening of Romeo and Juliet, where before the gang fight the Montagues were jostling each other and joking about sexual relations in the manner I expect from something like American Pie. Note also The Theater - most likely the theater R+J premiered - was built in Shoreditch and whose wiki states "this area in the "suburbs of sin" was notorious for licentious behaviour, brothels and gaming houses."

Ammianus Marcellinus railed against the popularity of vulgar Juvenalian satires instead of more elevated history or philosophy. Assessing modern opinion on Juvenal it's tough because his poetry is definitely not first rate, but he is widely appreciated and well liked for his dark humor and vivid pictures. Also, ancient satire as a genre is really popular today.