Answer
Salam (Peace) Dear Mary,
Thank you for your question and for contacting Ask About Islam.
One could fall into serious misconceptions if he or she picks a word out of context such as “Jews as pigs”, and jump to the conclusion that the Quran describes all Jews alone, past and present, as pigs, and then proceed to make three further jumps: The Quran is racist, Arab Muslims (who are mainly Semite) are anti-Semitic, and, finally, Islam is a violent anti-peace doctrine.
In the verse which gives the meaning of:
{Say: Shall I inform you of (him who is) worse than this in retribution from Allah? (Worse is he) whom Allah has cursed and brought His wrath upon, and of whom He made apes and swine, and he who served the Shaitan; these are worse in place and more erring from the straight path.} (Al-Maidah 5:60)
The meaning of the word swine (or pigs in other translations) should be explained in the context of the complete verse. Similarly, the verse should be interpreted in the context of the whole chapter (surah), and the whole issue should be understood in the framework of the whole Book (Quran) and the message (Islam). Further, one should be fully aware of historical facts and be alerted of common (forcibly publicized) stereotypes.
The reference in the verse is obviously to some who acted in a mischievous manner towards God, His messages, and Messengers. The rationale behind cursing some for their sinful stances and deeds could be gradually unfolded if you read through the preceding verses which give the meaning of:
{O you who believe! do not take for guardians those who take your religion for a mockery and a joke, from among those who were given the Book before you and the unbelievers; and be careful of (your duty to) Allah if you are believers. And when you call to prayer they make it a mockery and a joke; this is because they are a people who do not understand. Say: O followers of the Book! do you find fault with us (for aught) except that we believe in Allah and in what has been revealed to us and what was revealed before, and that most of you are transgressors?} (Al-Maidah 5:57-59)
Objective in-depth reading of the chapter and other parts of the Quran leads logically to the following:
The words “monkeys and pigs” here are not to scold or revile these persons; rather, they express condemnation of their deeds.
They do not condemn a specific race or a whole race, but only those whose mentality and conduct are as described. So, it is their deviation from the proper divine guidance that makes such individuals deserve to be turned into monkeys (behaving thoughtlessly) and pigs (neither bashful nor shy of wicked acts).
The deviations and blunders for which they deserved such severe descriptions are not only those referred to in chapter five (Al-Maidah) of the Quran, but are expounded in more details in chapter two (Al-Baqarah). Further examples can be traced in other scattered locations of the Quran, from which you can form a long list.
In listing these deviations, the Quran does not so much aim to discredit Jews or Christians as it serves five of the major objectives of Islam:
1. Emphasize the unity of the message of God which He sent to all His prophets and messengers, starting with Adam then Nuh (Noah), Ibrahim (Abraham), Musa (Moses) and Isa (Jesus); ending with Muhammad (peace and blessings be upon them all), and including all genuine prophets of God.
2. Remind mankind that all the messages of all the prophets prior to Muhammad have been tampered with: either lost, compromised with pagan beliefs, or intentionally distorted. Revealed texts were either neglected, modified, or replaced with human texts given the status of “holy” books.
3. Offer Islam—as presented in the Quran and the detailed guidance of the Last Messenger—to be the final universal message to mankind. Thus it was to be (and has been) preserved unchanged to the end of time.
4. Keep a permanent reminder and warning to those who accept Islam, not to repeat the mistakes of some of the followers of previous messages.
5. Present Islam as a universal message and an open invitation to all nations and all generations. Being a universal message, Islam does not recognize superiority for a particular race, color, or language; nor is it based on wealth, social status, or personal talents. Superiority is based only on sound faith, sincere obedience to God, pious behavior, and positive competition in all types of charity and good deeds. It is only along these scales that people are differentiated in Islamic law and in the Hereafter. 
Applying the guidance of this unique book, the Quran, the global nation of Islam was like a crucible, in which all races, cultures, and environments were fused into one unprecedented “global civilization.” It was the only genuine “global system” of unity, equality, justice, and welfare ever witnessed on this earth.
If you have any further queries, please do not hesitate to ask.
Salam and please keep in touch.