How much sexual symbolism is there really in the novel, and how clear/unambiguous is it?
There's certainly quite a lot of sexual and sexual-adjacent symbolism in the book, although I'm not sure that, as modern readers, we can shed much light as to how unambiguous it might be. Decades of scholarship on the book have made things that might once have been veiled relatively easy to uncover. But here are some examples:
The noise approached, came close, and a figure was apparently on the point of gliding past her when something tugged at her skirt and pinned it forcibly to the ground. The instantaneous check nearly threw Bathsheba off her balance. In recovering she struck against warm clothes and buttons.
Here, Troy's spurs have become caught in Bathsheba's skirts. This itself is symbolic in two ways. Firstly, he has entangled her both physically and by force of his good looks and gallantry. Secondly, it is clear that the spur could quite easily rip the skirt away.
But look also at the suggestive language in the passage: the skirt is "tugged" and "pinned forcibly". Bathsheba falls, prone and vulnerable. She discovers "warm" clothes. This continues all through the scene as Troy offers to "unfasten" her. Bathsheba "tugs softly" at the skirt. It's also worth noting that this episode occurs at night.
This evening Bathsheba was unusually excited, her red cheeks and lips contrasting lustrously with the mazy skeins of her shadowy hair.
Bathsheba was regarding him from the other side, still with parted lips and distracted eyes.
Her brow had heavily contracted; her whole face was pallid, her lips apart, her eyes rigidly staring at their visitor.
Something in the exact arch of her upper unbroken row of teeth, and in the keenly pointed corners of her red mouth when, with parted lips
There are a lot of references to Bathsheba's mouth and lips in the book. That, in itself, would seem symbolic enough. But look how they're described: "parted", "red", "excited". It seems clear that Hardy is encouraging us to think about Bathsheba as an actively sexual being. This in itself was pretty revolutionary for the Victorian era.
she lighted on a spot sheltered from the damp fog by a reclining trunk, where she sank down upon a tangled couch of fronds and stems. She mechanically pulled some armfuls round her to keep off the breezes, and closed her eyes.
Here, Bathsheba is sheltering in what turns out to be a mossy hollow, damp and warm. She rises from it in the morning and finds she has lost her voice. There's a parallel to be drawn here with gestation and birth, the baby finding itself voiceless and powerless after delivery. Other examples elsewhere in the book include Bathsheba's very clear state of arousal after kissing Troy and the whole sheep-shearing chapter with its primal, animalistic overtones.
It's also worth noting that the published version of the book was likely considerably less racy than the early drafts. Hardy was working under the supervision of Leslie Stephen, the editor of the Cornhill Magazine, who had invited Hardy to pen a serial for the magazine. Concerned about shocking his middle-class readers, he had Hardy revise substantial portions of the book to remove what he saw as salacious material. This suggests that Hardy was deliberately trying to push the boundaries of what was considered acceptable content at the time.
Was it clearly intended to be subversive with regard to cultural norms of the time?
Again, it's going to be a struggle to determine "clearly" in this case as we can no longer know the mind of the author, and what's clear to us might not have been clear to a contemporary reader. However, by contrasting Hardy with other authors of the time, an argument can certainly be made that he was indeed attempting to be subversive.
It was relatively common in novels of the era for a "happy" ending to involve marriage: look at Jane Austen's work for some examples. And Far from the Madding Crowd can be read as being part of this trend: through the course of the novel, Oak wears the wild Bathsheba down and the two are eventually married. Indeed some Victorian readers felt Hardy had gone too far and regarded the book as misogynist.
However, it's also possible to read Oak as a somewhat villainous character, and his "taming" of Bathsheba as negative. He deliberately evokes feelings of guilt and fear to press his case. He also shamelessly exploits the capitalist system to rise in social station to the point where he is able to court Bathsheba. He pursues her over the long term, despite her early and vigorous rejections of him, a behaviour we might characterise today as "stalking". In this reading, Hardy is subverting the "happy" ending of marriage by implying that the marriage will not be happy at all, but coercive.
How do we know this isn't just us reading the book through the lens of modern moral values? Well, we can't for certain. But there's a clue to be had in looking at Hardy's later work. Both Tess of the d'Urbervilles and Jude the Obscure paint far more critical pictures of the Victorian obsession with marriage. While people change their opinions over time, it's perhaps difficult to see how the apparent misogynist who wrote Far from the Madding Crowd could have become the stern critic of Victorian prudery and female oppression seen in Tess of the d'Urbervilles in the space of 15 years.
Was there any negative public reaction to this aspect of the novel?
It's hard to prove a negative but as far as I can tell, no, there was not. Indeed the novel was both a critical and commercial success. The only dissenting voices at the time appear to focus on the plot being vapid and unlikely. Henry James, for example, wrote:
Everything human in the book strikes us as factitious and insubstantial; the only things we believe in are the sheep and the dogs.
Summary
Taking the original question as a whole it seems there's enough evidence to suggest the answer is a cautious "yes" - it seems like Hardy was deliberately mocking the prevailing notions of sexuality at the time. There are a lot of allusions to active female sexuality in the book, there were originally more before his editor cut them, his heroine spends much of the plot rejecting the notion of marriage as happiness and Hardy's later work is considerably more clear in rejecting the established morality of his era.
References:
Leslie Stephen to Hardy, 8 Jan., 17 Feb., 12 Mar., 15 April 1874. In Richard L. Purdy, Thomas Hardy, a bibliographical study (Oxford: Clarendon, 1954, repr. 1979), pp. 336-341.
Rosemarie Morgan, Cancelled words: rediscovering Thomas Hardy (1992)
Rosemarie Morgan, Women and Sexuality in the Novels of Thomas Hardy (1988)
