No they won’t. Don’t flatter yourself or your religion. And no, churches in Denmark aren’t being forced to perform same-sex marriages.
The Church of Denmark is a state church, meaning it receives financial support from the government. When the government passed marriage equality, any institution receiving financial support from the government must perform same-sex marriage. However, there is a caveat in the law: priests opposed to same-sex marriage are not required to perform the ceremony; they simply direct the couple to a different church or priest who will perform the marriage. The LDS Church does not receive financial support from the government in Denmark and therefore is not required to perform same-sex marriages. Moreover, even if they did receive financial support from the government, they would simply direct the couple to a different church.
There is talk that the LDS Church is going to redefine marriage yet again. In fact, this redefinition would mean they will stop performing marriages altogether. Instead, they will refer to marriage (or unions) as a “sealing” and only perform sealings. If the talk is true, this might mean sealings performed in temples and marriages performed in meetinghouses will not be state-sanctioned. In other words, my marriage would be equivalent to an LDS marriage or sealing: none of us would receive any legal protection for having a ceremony. However, heterosexual (Mormon) couples could still obtain a marriage certificate from the state. This might be a good move for the LDS Church.
Regardless, even if things continue as is, the LDS Church won’t be required to perform same-sex marriages in temples or meetinghouses. Here’s why: they don’t even have to perform marriages for heterosexual members if they don’t want to. Couples who engage in pre-marital sex (even though they have the legal right to marry at a state level) aren’t allowed to marry in an LDS Church or temple. The fact that heterosexual marriage is legal does not dictate to the Church what they do within the Church. There is no reason to believe it is any different for homosexual couples.
Finally, remember how you’ve made gay and lesbian members feel unwelcome at church? They’re still going to feel unwelcome when same-sex marriage is recognized.
Will the legalization of same-sex marriage bring with it gay and lesbian members of the LDS Church who want to marry same-sex partners in the temple? No.