As anybody who spends much time with Orthodox Jews knows, it's forbidden for a Gentile to keep the Sabbath. The source for this is Sanhedrin 58b, near the bottom of the page:
ואר״ל עובד כוכבים ששבת חייב מיתה שנא׳ ויום ולילה ישבותו
And Resh Lakish said, "A non-Jew who keeps the Sabbath is subject to the death penalty, and the biblical proof text is 'And day and night they shall not (do some verb that obviously has the same root as "Shabbat").'"
The verb that they shall not do is
You can see the letters of the word "Shabbat" in it.
Whether חייב מיתה (subject to the death penalty) is meant literally is interesting, and the other words for "non-Jew" that appear in other editions of this text are interesting, but they're not what I want to talk about now. Out of its biblical context, this proof text looks pretty good. But let's look at it in its context, which is Genesis 8:22:
עֹד, כָּל-יְמֵי הָאָרֶץ: זֶרַע וְקָצִיר וְקֹר וָחֹם וְקַיִץ וָחֹרֶף, וְיוֹם וָלַיְלָה--לֹא יִשְׁבֹּתוּ
While the earth remaineth, seedtime and harvest, and cold and heat, and summer and winter, and day and night shall not cease.
(Copied and pasted from here.)
When we think about Resh Lakish's proof text, we notice two things right away: it has nothing to do with Shabbat, and it has nothing to do with non-Jews. We also note that he changed the meaning of "night and day"--in the proof text, it's an adverb saying when they shall not keep Shabbat; in the original verse it's a noun, listing some of the things that shall not cease.
I understand that Resh Lakish was operating in a different environment than we are. If you tried pulling this, I'd accuse you of being dishonest in your use of the verse.
So, a few questions, none of which I claim to know the answer to. Does it seem likely that Resh Lakish intended this to be an actual halakhah? And are contextomies like this usually considered valid as proof texts?
Many of us Orthodox Jews say things like "If only our non-Orthodox siblings would learn Torah with us, unless they're just being contrary, they'd choose Orthodoxy." Indeed? Among ourselves, we're more honest. If we point out something that's distasteful in Torah, we might get the response "It is distasteful. But it's Torah! What can you do!" To those who haven't accepted what we consider Torah, "But it's Torah" isn't a very convincing argument.
Anyhow, let's imagine someone decides to put us to the test--they decide to try learning Torah with Orthodox Jews. Let's imagine they happen into a discussion of the prohibition on Gentiles keeping the Sabbath. And let's imagine this person sort of generally accepts the Bible but has doubts about rabbinic Judaism--a typical religious non-Orthodox Jew (you should forgive the expression). So in this discussion, this person hears that Gentiles are subject to the death penalty if they keep Shabbat. Distasteful. But there's a biblical proof text. Interesting. Now let's imagine they check the proof text at home and discover that the text has been distorted. Why should this proof text that was good enough for Resh Lakish be good enough for a person living in our culture? "But he was Resh Lakish, and this is just some apikoros (I mean, we'd call this person a tinoq shenishba--a kidnapped infant--if they weren't so obviously an apikoros, which they obviously are, since they object to this proof text)." Well, OK, but we're claiming that an open-minded kidnapped infant is going to accept Orthodoxy if they learn Torah with us. If we claim that such a person is somehow being perverse by not accepting Orthodoxy after open-mindedly learning Torah with us, we're doing a petitio principii, as I always say--we're assuming the truth of what we were setting out to prove, which is logical cheating.