(Technically, the Brontë sisters didn't publish anonymously - they published pseudonymously at first as Acton, Currer, and Ellis Bell. I once saw a very early edition of one of the books - either Jane Eyre or Wuthering Heights - in a bookshop with the original Bell pseudonym, and it was incredible.)

The issue behind pseudonymous or anonymous publication did not have anything to do with the rights of married women - for one thing, all four of your examples were unmarried, at least while they were writing. (Charlotte Brontë did marry, and died while pregnant soon after.) Married women lacked legal standing because they were femes coverts, subsumed into their husbands' legal identities; unmarried women were femes soles, who could sign contracts. (I explain more about this in the seventeenth and eighteenth centuries here, linking to older answers by /u/sunagainstgold that go into even more detail.) Femes coverts weren't disallowed from signing contracts, either, as long as their husbands assented or had abandoned them. If a married woman were to sell a manuscript to a publisher without telling her husband and he found out, he might have gone to court to force the publishers to sell it back (or just pocketed the money his wife had earned on the sale, since it was legally his).

The main problem the Brontës and Austen faced was that women of their class background were not supposed to write for money - to do anything for money, really - and were not supposed to be known outside of their circles of acquaintance. All four were the daughters of clergymen and therefore firmly in the upper half of the middle class, even if all were stretched for income. Their position was supposed to be centered on care for the home and production of items for it: the time when the Brontë sisters were publishing was the beginning of the "golden age of domesticity", when there was a serious appreciation for the skills required in making a cake rise, getting linen white again, and gelling a jam, and an expectation that women would devote their time to said skills. It was understood that women who had not been "gently bred" might do wage work of varying dirtiness, depending on their specific circumstances, but if it were at all possible for a wife, daughter, or sister to be supported by the men or man in her life, she was not supposed to contribute monetarily to the family.

However, women did write and publish novels (and poetry and plays) and had been for some time. We can look back to the seventeenth-century Aphra Behn as the acknowledged field-opener, but while Austen was growing up and writing herself, there were a number of active or only recently-deceased female authors she would or could have been aware of. Many wrote semi-realistic novels in a more adventurous vein than Austen's own, or novels of sentiment: Frances Sheridan (The Life of Miss Sidney Bidulph), Eliza Haywood (Love in Excess, The Distress'd Orphan, The History of Miss Betsy Thoughtless, et. al), Frances Burney (Evelina, Cecilia), Elizabeth Inchbald (A Simple Story), Maria Edgeworth (Castle Rackrent), Charlotte Turner Smith (Emmeline), Laetitia Matilda Hawkins (Rosanne). On the other hand, Ann Radcliffe is one of the most famous Gothic novelists - her Mysteries of Udolpho (1794) was referenced directly in Northanger Abbey - and Clara Reeve was another early writer in the genre; later writers included Mary Shelley and Jane Webb, publishing a novel apiece in the 1810s (Frankenstein) and 1820s (The Mummy!), respectively. Lady Caroline Lamb, in the same generation, wrote several novels somewhere between Gothic and didactic fiction. I'm less familiar with authors of the 1830s and 1840s, the formative period of the Brontë sisters - I really like sentimental novels - but Anna Maria Hall (Marian), Rosina Bulwer Lytton (Cheveley), and Harriet Martineau (The Hour and the Man) are three; Elizabeth Gaskell (Cranford, North and South, Wives and Daughters) started publishing shorts in the 1830s and didn't publish a novel under her own name until the late 1840s, like Charlotte Brontë.

Remember the golden age of domesticity I mentioned before? That's tied into the changing attitudes towards women's behavior over this entire period, the late eighteenth through early nineteenth centuries (and especially the early nineteenth century): it was less and less acceptable for a woman to be a part of public life. That included writing, particularly if the writing was not morally didactic or instructional. The culture of highbrow salons and literary circles headed by and relatively welcoming to erudite women died off, and women made up a smaller proportion of published authors of fiction.

There's also another issue, though I'm not sure how many acknowledged it directly or acted based on it. Charlotte Brontë wrote (I'm not quite sure where originally, but it was reprinted as part of a Living Age article by Elizabeth Gaskell in 1851, and eventually in her Life of Charlotte Brontë in 1857):

... while we did not like to declare ourselves women, because – without at that time suspecting that our mode of writing and thinking was not what is called "feminine" – we had a vague impression that authoresses are liable to be looked on with prejudice; we had noticed how critics sometimes use for their chastisement the weapon of personality, and for their reward, a flattery, which is not true praise.

Essentially, Brontë wanted to avoid critics judging her fiction as a woman's work, either by going, "Aw, so cute and pretty and delicate," or by getting upset that it dealt with anything that wasn't cute and pretty and delicate. (Which they did - once it was known that the Bells were sisters, some criticized their novels as "coarse" for their frank references to dark realities of life.)