No.

The First Amendment articulated a limit on Congressional power. Congress may not pass laws about religious establishment (EG state churches, like the Church of England). Congress may not pass laws infringing on "the free exercise of religion." Congress may not pass laws that abridge "freedom of speech, or of the press." Nor may it pass laws preventing people from peacefully assembling and petitioning their governors.

However, state laws were another matter. Nine of the thirteen original colonies had established religions from their inception (Massachusetts, Connecticut, New Hampshire, New York, the Carolinas, Virginia, Maryland, Georgia). Four did not-- either they were "holy experiments" of religious toleration as colonies, or declined to establish a state religion in 1776 (New Jersey, Delaware, Pennsylvania, Rhode Island). So, in terms of religious establishment? In 1791, it was a state-by-state basis. The colonies did go through disestablishment, but very slowly over decades, with Massachusetts being the last (1832).

But suppose you were walking down the street in a state without an established religion, and you yelled "Hail Satan!" You could still face legal punishment for blasphemy.

Let me back up a bit. Today, most Americans think of agnosticism/atheisms as one legitimate option in the religious marketplace. This was not the case in the 1790s. Skepticism, atheism, and infidelity were the object of very fierce polemics. Historian Eric Schlereth characterizes this as "lived deism" (actual, existing deists, freethinkers, and heterodox figures) and "ambient skepticism" (a widely-shared conspiratorial belief that there were many secret, subversive freethinkers who would destroy national unity).

In the very broadest sense, early Republican political philosophy emphasized the formation of good public character. Create virtuous citizens, through education, the instilling of virtuous habits, etc., and you'd have a stable, functioning republic. Whether you were a Federalist, a Republican, a weird dissenter, whatever-- you understood that national unity depended on virtuous character. And religion* was thought to be essential to this process. Could atheists be virtuous? Could they be trusted? It was a question many American politicians, educators, novelists, merchants, and farmers debated at length.

During the 1760s-1780s, deism and even atheism a la Thomas Paine gained some traction in certain elite, Northeastern social circles. But US debates over the limits of religious toleration changed significantly after the French Revolution. Conservative cultural critics were aghast at the revolutionary violence, which they attributed both to uncontrolled republicanism and the natural consequences of atheism. Unvirtuous and uneducated people, no longer afraid of Hell and God's punishment, let their natural impulses run free and guillotined thousands! Surely this evident "Political Atheism" proved that individual atheists were, at best, good despite their ideal and not because of them. Blasphemous speech that incited people to abandon religion (and virtue) was politically dangerous, and should not be protected.

Of course, deists, freethinkers, and even some atheists like Abner Kneeland worked hard to counter the flood of anti-skeptical polemic, and the resulting state-level policy to protect "religion" against "infidelity." But these freethinkers were vastly outnumbered, both in terms of general populace and within policy-making positions. They often occupied privileged social positions (white, highly-educated men), so they used lyceum culture and print culture to make respectability bids.

For example: in the 1790s, you might walk down the street and hear a Freethinker on the corner explaining why Deism was reasonable, virtuous, protected women, ensured the stability of the family, and was politically good, actually. Or you might be offered a deist publication-- maybe Thomas Paine's scandalous bestseller Age of Reason (1794), the anti-religious work that ended his public career; or maybe something temperate like Nathaniel Dwight's Theophilanthropy, or the Spirit of Genuine Religion (1799). These public speakers hoped to show that deists, freethinkers, and "infidels" were trustworthy, virtuous citizens who should be allowed full participation in American civic life.

But if you shouted "Hail, Satan"? Not even the most liberal-minded deists would stick around to help you. (At least not for 40 more years, when Abner Kneeland takes legal aim at Massachusett's blasphemy laws).

Shouting "Hail, Satan!" would put you in the very worst social category of all: the village blasphemer. You weren't just questioning (corrupted forms of) Christianity, like a Unitarian, Quaker, or deist. You weren't even proclaiming that natural religion didn't need a creedal form. You were stating allegiance to the Devil. Probably ironically, but that was actually worse. It meant you had no religion. You're blaspheming publicly. You're destroying the religious values on which commerce and national unity depend. If you don't fear the Devil, and you don't fear Hell, how can we trust you to swear oaths of loyalty, or truthfulness? Or honor contracts? And what if the kids nearby overhear this mocking skepticism and imitate it? As Samuel Stilwell put the standard argument: "If nothing is to be believed... the present harmony that subsists in our religion and government would be upended."

For blaspheming in public, you could reasonably expect to be fined and maybe spend a night in jail. Once you emerged from prison, you could expect significant social obstacles that had not previously existed. Forget about whether the federal government could curtail your speech or not. Forget the state fine. You just torpedoed your reputation. Good luck finding work! (unless you have connections) And having a blasphemy charge on your record will make it pretty hard to introduce yourself to potential suitors. This is the best case scenario-- the one in which you're a young, able-bodied, educated, white man. You can play this off as a youthful folly-- a result of too much ale, or falling into bad company. Just be ready to explain to everyone why you're not that guy any more.

If you're female, I'm sorry to say that you've just told everyone you're a whore. It's a few decades before Frances Wright, the "Red Harlot of Infidelity," makes her appearance, and cultural commentators start wringing their hands over the "moral contradiction" of unsexed, masculine atheist women destroying the family. But even now, in 1791, you'll find many tracts about the kinds of women who incur blasphemy charges. Low women, women of loose morals, from poor, uneducated backgrounds, slinging "the filth and mud of blasphemy" at a religious happiness from which they're tragically debarred. Or careless coquettes, laughing at religion and chastity while foolishly hoeing around town, getting STDs, bringing shame to their dads, and making themselves unmarriageable.

Oh, and what if you're Black, or Indigenous, or Irish? Well, blasphemy is to be expected from course, lower natures, which have less capacity for reason and virtue. You'll probably be questioned about other vices. Are you drunk? Lazy? Have you swindled anyone lately? Did you run away from a master? In any case, you'll be statistically more likely to receive additional punishments, like a whipping or blasphemer's brand.

tl;dr: Freedom of speech/religion was constrained by state laws against blasphemy, and broader social attitudes towards infidels, skeptics, atheists, and freethinkers. You would be punished legally and socially for shouting "Hail Satan!"

*"religion" = a category in which Protestant Christianity was the "normal" center

The Bill of Rights, for a very long time, was only considered to be applicable to the federal government. The States themselves were free to, and often did, pass and enforce laws that went against what was outlined in the Bill of Rights. It wasn’t until the passage of the 13th, 14th, and 15th amendments during Reconstruction that the idea that the Bill of Rights could be applied at the State level in addition to the federal level came about. This concept is known as incorporation. The Supreme Court, over time, gradually began to adopt the concept of incorporation and apply the Bill of Rights to state law, in addition to federal law, when state laws were challenged in federal court. But for about a century after the passage of the Reconstruction amendments, the Court still allowed States to fragrantly violate fundamental rights guaranteed in the Constitution.

So, to answer your question, no. Despite this neat idea that your right to speech or religion was enshrined in the Constitution, States could very well have, and did, pass laws that restricted these rights. This was most notable in the South, where the States heavily regulated, or outright banned, anti-slavery literature in the press or in general. In fact, this is largely the reason why the idea of applying the Bill of Rights to the States through the Reconstruction amendments, specifically the 14th, became a thing. But it wouldn’t be until about the mid-20th century that the Supreme Court would completely do so, dragging their heels in the century after the passage of the Reconstruction amendments in applying them to State law.