The short and simple answer to your question is “yes.” A non-Jewish person may gift a tallit to a Jewish friend. However, I would recommend finding out if your friend already has a tallit, if she is accustomed to wearing one (not all women do) and what style, fabric, size, etc. she would like… a tallit is a very personal thing!
And, yet, there is perhaps a larger question behind your question: in what ways it is appropriate for Jews and non-Jews to support one another in their respective religious practices? This is not as simple as it might seem. The Jewish people has a long and complex history when it comes to interacting with the non-Jewish world. Indeed, Jewish law (halachah) has a lot to say about how we regard other religions and how we are supposed to interact with people outside our faith. I won’t review the history or sources here; but suffice it to say that relations between Jews and non-Jews have not always been positive and have evolved over the centuries in response to circumstances. All that being said, I want to reflect briefly on the contemporary situation.
Jewish people living in modern democracies like the United States today enjoy unprecedented freedom and are integrated into every aspect and sector of society. We are challenged to maintain our distinct religious culture while participating fully in the surrounding society. Healthy relations with non-Jews is very important. We are blessed to know our neighbors and befriend them. Jews have gained a great deal from being part of the larger culture and I believe the world has also gained a lot from the contributions of Jews and Judaism. Part of this friendship is sharing our culture and beliefs with others and learning about their faith as well. The question for me as a Jew is “how can I share my faith and practices with my non-Jewish friends and learn about their faith and practices while maintaining my boundaries and integrity?” So, my general rule is that I would not participate in the rituals of another religion in a way that violates or offends the beliefs of my religion; and I wouldn’t expect any different from my non-Jewish friends. But, to the extent that I can with integrity learn about and honor other faiths, it is incumbent on me to do so. There are ways we can support one another in our religious practice and other ways that we cannot – and as long as we can talk about it with honesty and respect, that’s ok.
What a wonderful thing to want to do! The giving of a piece of Judaica, especially a ritual item like a tallit, can be a very personal, intimate and kind thing to do. The tallit--worn at morning services and whenever the wearer is called up to participate in a service, as well as the entire day of Yom Kippur--is not just a fashionable garment, but one that speaks to the person's spirituality, even as it fulfills a mitzvah to wear fringes on the corners of one's garments in order to remember the commandments and observe them (Num. 15:37-41, parashat shelach lecha).
Tallitot can be expensive, so before making the investment, you may want to explore the following:
Is the lady in question traditionally observant? If so, she may not choose to wear tallit (traditionally, it was seen as a male garment and it's only been in the last 50 years that women have really taken up the practice).
Once, Tallitot came primarily in white, with a black, blue or white stripe. Now, they are a myriad of colors, shades, and styles, from very narrow stoles to large and dramatic capes. Get a sense of who this person is before acquiring one.
the blue stripe was to represent the blue cord that is described in Numbers. This shade of blue, called techeilet, ceased to be used when we as a people lost the technique to make the correct dye. Today it has been recovered, and occasionally you see a tallit with techeilet among the fringes. Is this lady going to want that or not (default is still for all the fringes to be white)? Do a little research.
You say this is for a 'single' lady. Is it for a life-cycle event for a teen, such as a bat mitzvah? If so, check in with the family as there may be a grandparent or other relative who has acquired a tallit, or there may be a family tallit that the woman will be wearing for the event.
As to whether a non-Jew may give a tallit: if your relationship with the lady is close enough and dear enough that you would feel it is appropriate to give such a gift, and you can answer the questions above appropriately, I say go for it!
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