Does Islam force people to embrace its teachings?

The Quran is very clear on this issue. The Quranic verse prescribing freedom of faith is of general import. In a literal translation, the verse is usually rendered as, "There is no compulsion in religion." However, a more expressive rendering would be, "No compulsion is admissible in matters of religion."
This meaning certainly applies to beliefs, as belief can only be the result of personal conviction. Therefore, it is totally against Islam to force anyone to accept the Islamic faith. We can only invite people to accept it, but the decision whether or not they do so is totally up to them. It is not the place of Muslims to punish them in any way if they choose to follow different faiths.
This was the practice of the Islamic State throughout history. If this applies to the basic principle of accepting God's Oneness, it applies even more clearly to matters of lesser importance, such as the implementation of certain Islamic rules. People should obey God's law because they believe in Him and hope to receive reward from Him and not because they are forced to do so.
And God Almighty knows best.