Answer
Wa `alaykum as-salam wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear Brother, we commend your desire to keep yourself well-acquainted with the teachings of Islam. May Allah help us all keep firm on the right path.
Muslims should always be keen on observing and consuming what is halal. With regard to kosher products, they are not all necessarily halal. If a kosher product contains any ingredients that are haram, the end product shall be considered haram either.
In response to your question, Sheikh Ahmad Kutty, senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Canada, stated,
Kosher products are halal only if they are free of ingredients that are considered haram, for it is not uncommon for even the foods served in hospitals as kosher foods to contain wine. Hence, even though these foods may be labeled kosher, they cannot be deemed halal for us to consume, because they contain wine.
So, not all kosher products are halal. Meanwhile, halal products are strictly made up of halal ingredients by the very definition of them.
If a certain yogurt contains gelatin derived from bovine, it is not sinful to consume it, as long as it is derived from cattle, even if the animal was not slaughtered in the Islamic way. If, however, the yogurt contains ingredients derived from pigs, then we should certainly avoid it. When in doubt, follow the following rule: Leave that which is doubtful in favor of that which is not doubtful.
However, we should not stretch this principle too far to the extent that we become too rigid, declaring everything as haram. Prophet Muhammad (peace and blessings be upon him) said, “Woe to those who are rigid.” (Muslim) He repeated the statement thrice. He also said, “This religion of ours is simple and easy; and whoever makes it rigid will only be overcome thereby.” (Al-Bukhari and Muslim)
Allah Almighty knows best.
Excerpted with slight modifications from Islam.ca.