Should public school elementary teachers teach about such holidays as St. Patricks Day, which have religious roots?
Yes! Most holidays have religious roots; the word “holiday” comes from “holy day.” Teaching and learning must be balanced to include a wide array of holidays representing many different cultures. It is essential that holidays are taught as information; the classroom is not the place to either promote or demote a particular culture. Be sure that information is factual and does not trivialize or demean through language, items, or actions.
I would say no, not because of the religious roots, but because of the problem of allocating time in elementary classes. Teachers need to look at what is required of them in each state, pick and choose three or four main themes, and teach deeply for understanding instead of teaching broadly.
We live in a diverse nation and students need to understand how that diversity is represented through the holidays we celebrate. If we ignore religious holidays, students have only a partial understanding of our richly diverse society and the many cultures that have contributed to our multicultural nation. The NCSS position statement on the study of religions points out that [I have made additions between brackets]: “Omitting study about religions [and their influence on holidays] gives students the impression that religions have not been, and are not now, part of the human experience. Religions have influenced the behavior of both individuals and nations, and have inspired some of the world's most beautiful art, architecture, literature, [holidays], and music.” (See the NCSS position statement, Study about Religions in the Social Studies Curriculum"). The clear distinction is not to teach religion but to teach about the religion particularly as it relates to the holiday so as to understand its significance.
In advance of such lessons, clearly communicate to families a clear rationale for what is taught and why, so there is no misunderstanding of your lesson objectives.