Exactly... It should not be dependent on the person's religion or religious beliefs but rather the person in general. Hence the criteria to marry someone or not should not be based on that alone. There are a whole lot more to the person than just his or her religious beliefs. However, having said that, a person's spiritual/religious inclinations does play a major role in the formation of their opinions I think.
Therefore, to conclude, I would say, to decide on whether to marry someone of another religion is a very broad question and should not be the only basis one makes one's decision to share a life with another. It may play a large role but is NOT the ONLY role! 
I would like to add on here that any interfaith marriages to be successful would very much depends on how both parties' mutual understanding and their workings on how they would want in not encroaching into each other's space and belief. They are such marriages that I have known were still successful till todate.
If any marriages require both partners to embrace the same religion whichever they select (well obviously, it will naturally follows the husband's faith) - wouldn't this denies the basic individual human rights?
http://www.urbandharma.org/udharma7/marriedlife.htmlA Happy Married Life - A Buddhist View
By Dr. K. Sri DhammanandaIndividual RightsOne of the causes of greatest concern among those who do not belong to the non-Semitic religions is the problem of conversion before marriage. While Buddhists and Hindus never demand that a couple must belong to the same religion before a marriage can be solemnized, many others tend to take advantage of this tolerance. Marriage, contrary to what many romantic novels say, does not mean the total and absolute merging of two people to the extent that each loses his or her own identity. When a religion demands that both partners must have the same religious label, it denies the basic human right of an individual to believe what he or she wants.
Societies throughout history have proved that "Unity in Diversity" is not only possible but desirable. Out of diversity comes greater respect and understanding. This should apply to marriage also. There are many living examples all over the world where the husband and wife maintain their own beliefs and yet are able to maintain their happy married life without confronting each other.
Buddhists do not oppose the existence of other religions even within the same household. Unfortunately this generous attitude has been exploited by unscrupulous religionists who are out to gain converts by all means.
Intelligent Buddhists must be aware of this stratagem. No self- respecting intelligent human being who really understands what he believes according to his own conviction should give up his beliefs merely to satisfy the man-made demands of another religion. Buddhists do not demand that their partners embrace Buddhism. Neither should they surrender their own beliefs.
Marriage is a partnership of two individuals and this partnership is enriched and enhanced when it allows the personalities involved to grow. Many marriages fail because one partner tries to "swallow" another or when one demands total freedom. According to Buddhism, marriage means understanding and respecting each other's belief and privacy. A successful marriage is always a two-way path: "humpy, bumpy" -- it is difficult but it is always a mutual path.Young people in this country and elsewhere sometimes think that "old fashioned ideas" are not relevant to modern society. They should be reminded that there are some eternal truths, which can never become out-of-date. What was true during the time of Buddha still remains true today.
The so-called modern ideas we receive through the highly glamorous television programs do not represent the way most decent people in the west think or behave. There is a vast "silent majority" of decent couples who are as deeply religious and "conservative" about marriage as any Eastern couple. They do not behave in the manner that the mass media has portrayed them. Not all the people in the west run off to get a divorce or abortion after their first quarrel or dispute.
Decent people all over the world are the same; they are unselfish and care deeply about those whom they love. They make enormous sacrifices and develop love and understanding to ensure happy and stable marriages. So, if you want to ape the west ape the "silent majority": they are no different from your decent neighbor who lives next door to you.
Young people must also listen to their elders because their own understanding about married life is not mature. They should not make hasty conclusions regarding, marriages and divorces. They must have a lot of patience, tolerance and mutual understanding. Otherwise, their life can become very miserable and problematic. Patience, tolerance and understanding are important disciplines to be observed and practiced by all people in marriage.
A feeling of security and contentment comes from mutual understanding, which is the secret of a happy married life.
