This fear is unfounded. Freedom of religion is a bedrock principle of our nation, protected in the First Amendment of the US Constitution, and in Article I, section 4 of the California Constitution. The California Supreme Court was explicit on this point in their decision. Here is a quote from the Supreme Court's opinion:
Finally, affording same-sex couples the opportunity to obtain the designation of marriage will not impinge upon the religious freedom of any religious organization, official, or any other person; no religion will be required to change its religious policies or practices with regard to same-sex couples, and no religious officiant will be required to solemnize a marriage in contravention of his or her religious beliefs. [Ca. Sup. Ct., S147999 (2008), p. 117]I would add that just as freedom of religion is still in effect, so too is freedom of speech. Churches continue to have full freedom to make their own decisions about whether to perform same-sex marriages, and to give voice to their own beliefs about the morality or immorality of same-sex marriage.
Myth: Churches may lose their tax-exempt status if they don't perform same-sex marriages, or if they advocate against it.
Some churches are nervous these days because the IRS has been investigating whether they have crossed a line into political advocacy, which would jeopardize their tax-exempt status. A recent organized protest called "Pulpit Freedom Sunday" had a few dozen pastors around the country endorsing presidential candidates from the pulpit. But the federal law is clear on what churches may and may not do in the political arena, while keeping their tax-exempt status. Churches and their leaders may speak freely on issues of public policy, even on specific legislation, and may encourage their members to support or oppose specific legislation, so long as they are not supporting a particular political party or candidate for office. They may spend an "insubstantial" (typically taken to mean less than 10%) amount of their funds on issue advocacy. The law strikes a reasonable balance, giving churches wide latitude to speak out on issues that they believe have moral or religious ramifications, while keeping them out of full-throated politics. (And also remember that churches are free to embrace full-throated politics if they wish, just not with a taxpayer subsidy for their donations.) Thus, no church or religious group will have their tax status penalized for advocating for or against same-sex marriage, or for supporting or opposing a particular proposition.
Given that churches are free to advocate against same-sex marriage while remaining tax-exempt, they are certainly not going to lose their tax-exempt status for refusing to perform same-sex marriages, if that is their belief.
It should also be noted that tax-exempt status is a matter of federal law, determined by the IRS. Thus, changes in California state law regarding same-sex marriage could not possibly have any relevance to the federal matter of tax-exempt status.
Myth: A legal policy of recognizing same-sex marriage is an assault on religious beliefs.
Some people feel that California's recognition of same-sex marriage imposes a redefinition of a religious principle, and thus is interfering in religion. However, it must be recognized that the term "marriage" has been used for a religious ceremony and a legal status, which may be related, but are not the same thing. It's possible to go to city hall and get married legally but not religiously. It's also possible to have a religious marriage but not get a state license (elderly couples remarrying later in life sometimes do this to avoid the legal complications). It's also possible for a marriage to end at different times in the eyes of the church and the state. For example, the Catholic church does not recognize divorce, so Catholic couples may get a legal divorce, but still be married in the view of their church. The state has its definition of marriage, and the churches have their definitions, and they're not always completely in synch. But it's a workable arrangement for a pluralistic society like ours. Thus, the state is defining marriage for the state's own purposes, while the churches are free to define marriage in their own way. The state's recognition of same-sex marriage is not imposed on churches any more than the state's provision for divorce is imposed on churches that don't believe in divorce.
It also must be said that not all churches oppose same-sex marriage. Some churches perform same-sex wedding ceremonies, and welcome and affirm same-sex couples. National denominations including United Church of Christ, Unitarian Universalist Church, Reform Judaism and others bless same-sex marriages as a matter of denominational policy. Other denominations, including the Episcopalians, Methodists, Lutherans, and Conservative Judaism, while lacking national consensus, have some churches and some clergy who have blessed same-sex marriages. Thus, a legal policy that would outlaw same-sex marriage is a disparagement to those religious institutions. Why should those religious marriages not merit equal recognition to all other marriages?
Further, it should be noted that even some religious leaders who oppose religious same-sex marriage also oppose unequal legal treatment for same-sex couples. California's top Episcopal bishops (who are themselves divided on whether their church should actually perform same-sex marriages) all came out in opposition to Proposition 8. And while the Adventist General Conference opposes same-sex marriage, a petition of Adventists opposing Prop 8 on the principle of religious liberty (something Adventists are quite sensitive to) has drawn endorsements from many pastors, professors, and other Adventist leaders.
UPDATE: There is a good discussion of the "scary" court cases being hyped out of context by Prop 8 supporters, as well as Q&A about concerns from a Christian perspective on the website for Adventists Against Prop 8.