Again I say that I do not agree with the wording of this flyer. Attacking a person's religion, even by a member of the same religion, is fundamentally wrong. I do not, and never will, condone ad-hominem attacks in politics. Attack the issue, not the person.
I have found very little evidence, both historically and scripturally that gun control is anymore or any less a Jewish issue than it is a liberal issue. The Jewish faith places a great emphasis on social justice and repairing the world. Many of it's views are similar or inline with the Democratic party. I believe that many people assume that because so many of the views match, it must be a Jewish issue as well. It is not.
Doesn't the Torah forbid guns?
In the Talmud, Shabbat 63a, it states that you shall not wear a sword on Shabbat. This is based on the idea that nations will beat their swords into plow sheers.
Additionally in Bava Kama, Rabbi Nathan states that you should not keep a dangerous dog, even if it is chained, for you do not wish to bring blood upon your house.
The first verse appears to apply only to Shabbat and the second is an opinion of Rabbi Nathan. It is an interpretation of a Torah verse "You shall bring not blood upon your house." Deuteronomy 24:8
There is certainly a risk associated with gun ownership, and in an ideal world it would not be necessary. But is this all that is said of weapons and self defense?
What does the Torah say about Self Defense?
Life is sacred, and must be protected above all else. What happens though, when one must choose between "his life or my life?" An answer is provided in Exodus 22:1
If, while breaking in, a thief is discovered, and struck and died, it shall be as if he had no blood.
In simple language, if a thief is killed breaking into your home, there is no guilt upon you or your house. Blood is used to refer to the blood guilt mentioned in Deuteronomy 24:8. The Torah provides here an exception here.
Further, the Torah tells us in Leviticus 19:16
neither shall thou stand against the blood of your neighbor
This commandment is interpreted as requiring a Jew to defend someone he/she sees being attacked. Since Jews are commanded to help others, and since life must be protected, the best possible tool must be used. There is perhaps no better tool to defend life and property than the gun.
What about the "sunshine" mentioned near Exodus 22:1
There is a passage related to Exodus 22:1 that states you shall not kill him if the sun rises upon him. Rabbi Solomon bar Iaasc (Rashi) tells us that this is intended as a metaphor. The sun raise refers to the home owner becoming aware that the criminal is not there to harm the home owner. The intent must be clear, such as the criminal surrendering or running away.
More about the Dog in Rabbi Nathan's example
Earlier, we read Rabbi Nathan forbad keeping a dangerous dog. There are several other Rabbinic opinions that state it is permissible to keep a dangerous dog if he is kept on a leash during the day. This was said to apply in dangerous areas. We could easily extend this example to keeping a gun holstered during the day, with the safety on. Additionally, some dangerous area may require the dog to be caged in the yard, but unleashed at all times.
Of Guns and Nazi's
One often overlooked aspect of Jewish attitudes towards guns and self defense is Nazi Germany. Hitler was quick to disarm the Jewish population. Since the Jewish population was required to register, it was easily to determine who the police should visit to confiscate guns. Once disarmed, the Jewish populations had no way to defend themselves against what was coming.
Today, we are seeing states requiring gun owners to register, to obtain special permits, and the government keeping lists of who owns guns. While there is not currently a huge threat to the people such as in pre-world war 2 Germany, the price of freedom is eternal vigilance.
Conclusion
The world is a dangerous place today. Jewish people are commanded to make this world a better place. Social justice and Environmental protections are essential to making the world a better place. Protecting our lives and our neighbors and friends lives are also paramount. As you can see, gun control is at odds with Jewish thought and is certainly not a Jewish issue.
One day, G-d willing, the world will beat its swords into plowsheers and peace will reign. Until that day though, we must arm ourselves with the best possible tools to protect life.
Source Materials
The Torah and Self Defense
Of Weapons and Wickedness