If you want to sue them, you should start with the US Constitution (as a model), in particular the Free Exercise clause: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof". The question is whether one could overturn homicide statutes on the grounds that an individual holds to traditional beliefs that a human sacrifice is required every few months. Or, is it an unconstitutional prohibition of the Mormon belief in polygamy to outlaw polygamy, see Reynolds v. US, 98 U.S. 145. The court held that
the statute immediately under consideration is within the legislative
power of Congress. It is constitutional and valid as prescribing a
rule of action for all those residing in the Territories, and in
places over which the United States have exclusive control. This being
so, the only question which remains is whether those who make polygamy
a part of their religion are excepted from the operation of the
statute. If they are, then those who do not make polygamy a part of
their religious belief may be found guilty and punished, while those
who do, must be acquitted and go free. This would be introducing a new
element into criminal law. Laws are made for the government of
actions, and while they cannot interfere with mere religious belief
and opinions, they may with practices. Suppose one believed that human
sacrifices were a necessary part of religious worship; would it be
seriously contended that the civil government under which he lived
could not interfere to prevent a sacrifice?
Observe that a religious exception to the law would be unconstitutional, as establishing religion as a means of gaining extra rights. The reductio ad absurdum of the unfettered religious-belief excuse is:
Can a man excuse his practices to the contrary
because of his religious belief? To permit this would be to make the
professed doctrines of religious belief superior to the law of the
land, and, in effect, to permit every citizen to become a law unto
himself. Government could exist only in name under such circumstances.
The "wall of separation" was modified more recently in the 60's and 70's. In Wisconsin v. Yoder, 406 U.S. 205, the issue was compulsory education imposed on Amish children, where higher education was held to be antithetical to the Amish doctrine of a simple life. The court rules that
The State's interest in universal education is not totally free from a
balancing process when it impinges on other fundamental rights, such
as those specifically protected by the Free Exercise Clause of the
First Amendment and the traditional interest of parents with respect
to the religious upbringing of their children
it was incumbent on the State to show with more particularity how its
admittedly strong interest in compulsory education would be adversely
affected by granting an exemption to the Amish
There were additional holdings pertaining to the legitimacy of the purported belief (that is, is there really such a doctrine – clearly yes). You might have better luck purporting to be a Rastafarian or Hindu, so I will set aside that complication.
The core question will be whether the government has a "compelling interest" in the restriction, also whether the restriction is narrowly tailored. In the case of Sherbert v. Verner, 374 U.S. 398, Sherbert's employer required her to work 6 days a week (a change in policy during her time of employment), which she refused to do (as a member of SDA) and was fired. Sherbert was denied unemployment benefits because the firing was for cause. The court ruled that
Disqualification of appellant for unemployment compensation benefits,
solely because of her refusal to accept employment in which she would
have to work on Saturday contrary to her religious belief, imposes an
unconstitutional burden on the free exercise of her religion.
There is no compelling state interest enforced in the eligibility
provisions of the South Carolina statute which justifies the
substantial infringement of appellant's right to religious freedom
under the First Amendment.
Employment Div. v. Smith, 494 U.S. 872 brings us to the neighborhood that you are interested in living in. The relevant detail is that Smith (and Black) were fired for ingesting peyote in connection with a ceremony at a Native American church. The court ruled that
The Free Exercise Clause permits the State to prohibit sacramental
peyote use, and thus to deny unemployment benefits to persons
discharged for such use
To be more precise,
Although a State would be "prohibiting the free exercise [of
religion]" in violation of the Clause if it sought to ban the
performance of (or abstention from) physical acts solely because of
their religious motivation, the Clause does not relieve an individual
of the obligation to comply with a law that incidentally forbids (or
requires) the performance of an act that his religious belief
requires (or forbids) if the law is not specifically directed to
religious practice and is otherwise constitutional as applied to those
who engage in the specified act for nonreligious reasons.
We can contrast this with Lukumi v. Hialeah, 508 U.S. 520. The city of Hialeh passed an ordinance forbidding animal sacrifice, specifically to suppress the Santeria church. The Supreme Court said, no, you may not do that:
Under the Free Exercise Clause, a law that burdens religious practice
need not be justified by a compelling governmental interest if it is
neutral and of general applicability. However, where such a law is not
neutral or not of general application, it must undergo the most
rigorous of scrutiny: It must be justified by a compelling
governmental interest and must be narrowly tailored to advance that
interest. Neutrality and general applicability are interrelated, and
failure to satisfy one requirement is a likely indication that the
other has not been satisfied
The ordinances' texts and operation demonstrate that they are not
neutral, but have as their object the suppression of Santeria's
central element, animal sacrifice.
At least so far, restrictions on drug use have not been overruled as conflicting the the Free Exercise clause, although if e.g. Washington state were to prohibit Mormons from purchasing marijuana (where others can), that would surely be struck down as unconstitutional.
There are a number of other relevant developments, for example Congress passed the Religious Freedom Restoration Act in 1993, in reaction to Employment v. Smith, and that law statutorily mandating that strict scrutiny be applied to the question of whether a law violates the 1st: but this was ruled unconstitutional as applied to the states in City of Boerne v. Flores, 521 U.S. 507. Then in Gonzales v. O Centro, 546 U.S. 418 (Schedule 1 tea for religious purposes), the court ruled that
The courts below did not err in determining that the Government failed
to demonstrate, at the preliminary injunction stage, a compelling
interest in barring the UDV’s sacramental use of hoasca
which is to say, we have a case where the federal government was prohibited from enforcing a drug prohibition involving religion.
A challenge of the type which you have in mind will surely also involve the question of the legitimacy of the purported religion, where UDV was founded in 1961 whereas one might suspect that your claimed religion is a pretext to smoke pot (hence the Rastafarian suggestion). The WWII era conscious objector cases held that the CO exception to military service is not limited to governmentally-approved religions, but as a general rule, the courts have not ruled that you can simply claim to have a religious belief which is being infringed on and thereby be excempt from the law. The basic issue would be whether either the US government of the state of Kentucky have a compelling interest in preventing the use of marijuana. The Kentucky Supreme Court does indeed recognize the concept of "strict scrutiny", so the case is not doomed from the start.