Racism is an LGBT issue. There are LGBT people of color, who are doubly discriminated against both by the LGBT community, and by their 'racial community'.
Immigration status is an LGBT issue. Not only are laws like Arizona's "Papers, Please" affecting LGBT people of immigrant backgrounds, many 'T's do not have documentation that match their gender presentation due to various legal hurdles. Thus they could face jail time for having incorrect papers, or perhaps even deportation. It also affects bi-national families. If one partner in a gay family is from the US, they cannot sponsor their same-sex partner for citizenship like an opposite-sex couple can. The non-American partner then faces deportation when their visa is up, leaving the American partner to make the heartwrenching decision about breaking up the relationship or out-migrating to another country. This is why we need the Uniting American Families Act.
The economy is an LGBT issue. Despite popular myth, LGBT people tend to be at the bottom end of the earning spectrum, transpeople especially. In 31 states it is legal to fire employees simply due to their orientation or transition status, regardless of job performance or other qualifications.
There are many ways that the LGBT community fits into other groups of "us"es. Not only do we need to stand up and speak out about wrongs done to gay people, we need to speak out against injustice, period. No one is safe until we're all safe. We're all in this together. Remember Martin Niemoller's poem:
"THEY CAME FIRST for the Communists,
and I didn't speak up because I wasn't a Communist.
THEN THEY CAME for the Jews,
and I didn't speak up because I wasn't a Jew.
THEN THEY CAME for the trade unionists,
and I didn't speak up because I wasn't a trade unionist.
THEN THEY CAME for me
and by that time no one was left to speak up."