G. B.,
Not every branch or denomination within Judaism shares the same views on sexuality or gender identity. Reconstructionist, Reform and Renewal are the most welcoming and accepting. Conservative has made halakhic decisions, some more positive than others, with regard to LGBT Jews. These four denominations/movements will ordain openly gay Jews; clergy affiliated with them are permitted to officiate at same-sex weddings. Orthodoxy is split, with some Orthodox lay leaders and rabbis being more welcoming than others, embracing more progressive halakhic opinions than others.
But to choose between one's religion and one's sexuality is not an easy choice for many. (Not even for those "choosing" religion via their interfaith relationship.) Thankfully, there are supportive organizations working towards the inclusion of all Jews, regardless of sexual orientation or gender identity, in our communities. For more information, you might take a look at
Keshet's resource or the
Jeff Herman Virtual Resource Center.