Yeah, they have the same rights indeed. They have the rights to live peacefully without any attacks from the society. They have the rights to work, eat, sleep, etc just like other "normal" people. But, same sex love isn't justified by the Bible
So, i guess we still have to uphold their rights. Respect them, befriend them, and show them the love of Christ. That's how they know that they're actually accepted by the people who were once sinners, but with the grace of God, finally gain salvation.
Jesus told us to hate sins, but love sinners (i forgot where this verse is, but my mom told me that it is in the Bible). How do we make them realise that what they do is wrong? We have to show them the love of God. How? By treating them the way we want to be treated. Remember, the Bible says that Jesus often ate with sinners. Why? because He wants to show His love. How can we expect them to accept Christianity (which says that LGBT are sinners) if we don't act like Christians are supposed to do?
Even when what you say is offending many people, i guess that's alright. Like what the Bible has said, we are lights in the middle of darkness.
So i guess as Christians, we have to uphold their rights by respecting them. That's how they feel accepted and loved. And that's how they know where true love comes from, Jesus Christ.
I respect LGBT because I want to uphold humanity. I don't support them because I am devoted to Jesus Christ