David Bahati, the sponsor of Uganda’s notorious Anti-Homosexuality Act (AHA), announced this weekend that he intends to reintroduce the bill in parliament, after a court found it invalid for procedural reasons last August.

But this time will be different. President Yoweri Museveni is under heavy pressure not to once again invite international condemnation by supporting it. More importantly, the Ugandan coalition opposing it is broad-based and deep.

In fact, American activists could learn a lot from their Ugandan counterparts.

On a recent trip to Uganda, I met with local LGBT activists – and one lesson consistently emerged as key to their strategy: the fight for LGBT rights must be situated within a broader campaign for human rights and civil liberties.

For example, I met with Adrian Jjuuko, Executive Director of Human Rights Awareness and Promotion Forum. He’s a young, energetic attorney whose office is lined with case binders from major LGBT rights cases he has helped win. That includes the successful lawsuit against Rollingstone Magazine for publishing a front-cover headline advocating that key LGBT activists be hung, and the most recent case that led to the nullifying of the AHA. Jjuuko has been on the front lines of the fight since graduating law school only six years ago.

Jjuuko told me that a strong civil society foundation – including freedom of speech and assembly, due process, and privacy protections – is critical to the LGBT community. LGBT rights cannot advance in Uganda if in general, unpopular minority views are squelched in the press, non-governmental organizations run the risk of being shut down if they disagree with the government, and police abuses such as unjust detentions and lack of due process are commonplace.

“The LGBT community must lift itself up with everyone,” Jjuuko said. “Otherwise, we will all be stuck in the same quagmire.”

Jjuuko cited the work of the Black Monday movement, an anti-corruption movement in Uganda, as one example of this broad-based effort that LGBT groups can join to strengthen civil society and good governance generally. And that broader context must include economic development. As Jjuuko put it, “What good are LGBTI economic rights if no one in the country can afford salt?”

Another example is the Civil Society Coalition on Human Rights and Constitutional Law, made up of diverse Ugandan organizations, including non-LGBT organizations that coalesced to oppose the earliest version of the bill in 2009.

This is how the early American LGBT movement began as well. It focused not solely on the equal rights of LGBT people, but on the constitutional liberties that all U.S. citizens – including LGBT people – are supposed to enjoy. For example, the first LGBT victory at the U.S. Supreme Court was not about sodomy laws or marriage equality, but free speech. That decision, One v. Olesen (1958), barred the U.S. Postal Service from prohibiting the mailing of One magazine, one of our first gay and lesbian magazines. (Ahead of its time, the cover of its first issue bore the headline “Homosexual Marriage?”) Through the strengthening of free speech rights, the nascent gay and lesbian community could begin to connect and grow nationally.

In the 1970s, Harvey Milk connected LGBT rights with labor rights when he worked with unions to organize a boycott of Coors beer in Castro Street bars. While Milk and other LGBT activists were incensed by Coors’ practice of forcing prospective employees to undergo a polygraph test to determine whether they were gay (and refusing to hire those who “failed”), Milk also understood that failing to change Coors’s overall anti-worker policies would only leave LGBT workers vulnerable if and once they were hired.

As the LGBT movement developed, the focus shifted to equal rights for LGBT people specifically. This was justified in its time: equal treatment and protection of LGBT people under the law (removing all “gay exceptions” from the books) is essential to equal citizenship and dignity. However, as we begin to move beyond formal equality in the law in some areas of the country, we must also broaden our sights if we truly are to achieve equal justice for the LGBTQ community.

For example, activists cannot work on LGBT criminal justice alone without addressing the larger problem of racialized police misconduct and brutality that plagues so much of America, as recently illustrated in Ferguson. (The organization I direct, GLAD, was born out of defending gay men from targeted police sting campaigns in 1978 and continues to work to monitor the excessive policing of our community, particularly gay men and trans individuals.)

Likewise, there is a crisis regarding affordable legal representation in our country, with 50 percent of civil litigants seeking free legal services being turned away. Without adequate and affordable legal representations for everyone, including LGBT people (who are disproportionately poorer than the general population), all of the new legal rights and protections that have been achieved will simply remain words on paper.

LGBT activists in Uganda and elsewhere understand the critical need to raise the floor for everyone if specific gains for LGBT rights are to be meaningful. But we need not look as far Uganda for these lessons. As portrayed recently in the movie Selma, MLK rightly asked the question: “What good is having the right to sit at a lunch counter if you can’t afford to buy a hamburger?” Social justice advocates here and abroad are responding to that question with renewed energy and conviction. The question for the U.S. LGBT community is whether we will too.

Janson Wu is the executive director of GLAD (Gay & Lesbian Advocates & Defenders).