No
House Bill 164 or the "Ohio Student Religious Liberties Act of 2019" has been passed by the House and awaits on a vote by the Senate.
It covers several areas guaranteeing the freedom of religious expression. The part closest to the claim is Section 3320.03:
No school district board of education...shall prohibit a student from engaging in religious expression in the completion of homework, artwork, or other written or oral assignments. Assignment grades and scores shall be calculated using ordinary academic standards of substance and relevance, including any legitimate pedagogical concerns, and shall not penalize or reward a student based on the religious content of a student's work.
"Religious expression" is explained:
As used in sections 3320.01 to 3320.03 of the Revised
Code, "religious expression" includes any of the following:
(1) Prayer;
(2) Religious gatherings, including but not limited to prayer groups, religious clubs, "see you at the pole" gatherings, or other religious gatherings;
(3) Distribution of written materials or literature of a religious nature;
(4) Any other activity of a religious nature, including wearing symbolic clothing or expression of a religious viewpoint, provided that the activity is not obscene, vulgar, offensively lewd, or indecent.
This is probably what you already imagine to be the case.
A student's book report on the Bible or the Koran or the Book of Mormon would be graded purely on it meeting the applicable academic standards and not on the choice of religious literature.
When asked "when is the Cenozoic Era", the answer "5,000 years ago" is marked wrong, as that is not correct by "normal academic standards".
The sponsor of the bill Rep. Ginter agrees.
Under House Bill 164, a Christian or Jewish student would not be able to say my religious texts teach me that the world is 6,000 years old, so I don't have to answer this question. They're still going to be tested in the class and they cannot ignore the class material.
In fact, this bill is so much a "status quo" legislation, that even its opponents label it "redundant and unnecessary" (opponent Rep. Ingram).
It's not uncommon for politicians pass such laws duplicating existing ones, for the emphasis and political credit.