When saddling up my social justice steed (his name is Binky), I find it helpful to keep two things in mind:
1. People are pretty much the same
People are just people, you know? They sleep and eat and worry and poop and gawp at the stars and try to do good things, not do bad things, and not put socks in toasters. They fret about their loved ones and fight with their partners and try to make their lives better, whether they are Bedouin ladies living in the Jordanian desert*, or my mother.
It's easy to demonise people when you can put them in a little box marked Other, and see them as entirely defined by the thing that makes them different to you - as if all of the man-gays spend literally 100% of their time having massively gay sex up the chuffer, and all Muslims are just 'all pray all the time'.
Basically, if someone seems to be THE EMBODIMENT OF ALL EVIL, or REPRESENTING THE DOWNFALL OF CIVILISATION, think about them making a sandwich.
"This DASTARDLY FORNICATOR will BRING DOWN HUMANITY by his INIQUITOUS PLAN to MARRY SOMEONE OF THE SAME GENDER! GARRR!"
"His name is Jeff. He and his partner Simon just had a terse exchange of emails about whose turn it is to buy loo roll."
"Erm, EEEVIL... no, I've lost it."
* THIS IS SO AWESOME. WATCH IT. IT WILL FILL YOUR HEART WITH WONDER AND JOY.
2. People are not all the same
And yet! The fact that something is true for you does not mean it is true for everyone else on the planet. For instance, the original version of that sentence above was 'They sleep and eat and worry and lust...' before I remembered, hey, asexual people exist! Something which I see as absolutely fundamental to The Human Condition is in fact completely irrelevant to a significant chunk of humanity. A gentleman may be overjoyed at being approached by an alluring stranger in a lift - but with the situation reversed, a woman is more likely to be edging towards discomfort, if not terror, at being hit on by a guy in an enclosed space with no escape route. Just because I imagine I would find wearing a niqab uncomfortable and demeaning, doesn't mean that's how Muslim ladies who choose to wear it feel.
You can fill in your own examples, I'm sure. People are pretty much the same, despite superficial differences! Also, people are different from each other, and you don't know how they feel about stuff until you ask them! Both true. Both important.