In a two-party system, very few people agree with every tenet of their party's platform. There are religious people who support the Democratic Party, despite the Democrats' general opposition to religious values. There are atheists who support the Republican Party because they agree with the basic principles of laissez-faire economics. The only hypocrisy with regard to Cheney is the hypocrisy of her opponents, who champion the right to self-expression but refuse to allow homosexuals to express their value preferences when those preferences do not toe the liberal line.
The answer to the second question is similarly simple: The Republican Party has no duty to stop Cheney from campaigning on its behalf. Conservatives believe that her lifestyle is immoral, regardless of her political stance. Homosexuality is wrong. Bringing up a child in a homosexual household is similarly wrong. A child deserves a mother and a father; "Heather Has Two Mommies" may, unfortunately, be descriptive in many states, but it shouldn't be the standard. For a lesbian to artificially inseminate herself, knowing full well that the child will be brought up in a home lacking the basic component of fatherhood, is disreputable.
But Cheney does not ask the Republican Party for permission to act as she does in her personal life. She does not campaign for Republicans on the condition that the Republican Party change its moral and political stance with regard to homosexuals. Is her behavior inappropriate? Absolutely. But the behavior of many prominent Republicans stands in stark contrast with the party platform. The GOP stands opposed to abortion; surely there are many women who vote and campaign Republican who have had abortions in the past.
Only when those like Cheney begin dictating policy to the Republican Party does the party have a responsibility to choose between the support of homosexual Republicans and its traditional moral platform. In the last presidential election, for example, the Log Cabin Republicans refused to endorse President Bush; the Republican Party responded by ignoring the LCRs. There, the LCRs forced a choice, and the GOP chose its values over a certain segment of its voters. Cheney has yet to force such a choice. If and when she does so, the GOP will be obligated to sacrifice her support for its principles.