For a long time, I've been looking for the difference between "proscribe" and "prohibit". Unfortunately, I couldn't find any exact answer to my question, though I inferred from a passage that "prohibit" is related to law.
A quick look at usage shows that the two terms are used pretty much interchangeably.
If there is a difference, it is that proscribe is used in situations where specific actions, substances, persons, or organizations are to be placed outside the protection of the law.
Proscribing actions or substances in effect prohibits them. Proscriptions against people or organizations work a bit different. A person can be prohibited from being lawfully present in a geographic area by a proscription. Organizations can be prohibited from conducting meetings and recruiting members by proscription.
The main difference between the words is that prohibit always carries the sense that the action is forbidden by some authority.
Proscribe, on the other hand, can mean "denounce or condemn", which doesn't mean that it has been outright forbidden, just very strongly disapproved, though it usually means prohibited, too.
Also, proscribe can apply to a person, while prohibit does not do so.
Other answers have addressed nuances of meaning, so I'll add more on usage. Looking in the Corpus of Contemporary American English, prohibit is much more commonly used: it occurs almost 40 times as often as proscribe.
So, if choosing between the two, prohibit would be a more familiar choice.
Some examples from COCA:
Egregious use of hateful words can be punished under most existing codes that proscribe harassment, intimidation, or threats of violence. [Magazine]
Marxist teaching does not proscribe religion, but rather considers religion to be primitive and superstitious, and predicts that religion will tend to disappear... [Academic]
Six states and the District of Columbia broadly prohibit employers from discriminating on the basis of breastfeeding activities... [Academic]
...the U.S. Department of Education will propose rules that will prohibit certain colleges from receiving federal financial aid... [News]
In many cases, prohibit can be substituted for proscribe, but it doesn't always work the other way around. While both words are transitive, with prohibit, we can disallow either the thing, or a person from doing the thing. We most often proscribe the thing or behavior. The only example I found in COCA of proscribing a person from doing something was an instance of proscribe military personnel from voting. So, proscribe discrimination is fine, but ? proscribe employers from discriminating may not sound right.