The other day I was talking with someone about the BLM disruption of the Toronto Pride parade. He was surprised that it happened because he figured Pride must already be incredibly inclusive and sensitive to racial issues - after all, since queer people are persecuted, they must really understand racial persecution and stand against it, right?
It is an easy mistake to make, but it is still a mistake.
There are no end of gay people who are really racist. Same goes for disabled people being homophobic, or people of colour being ableist. Of course all the other permutations apply too, these are just an illustrative cycle. (Not that I am saying that minority groups are more bigoted than the general population - just that I don't think there is much difference.)
Just because a group is oppressed or attacked does not make them more sympathetic to others who have similar issues. Just look at all the brutally racist, sexist, Islamophobic atheists on the internet. (I despise religion, but scapegoating Islam as 'the bad religion' is bullshit.) Atheists are mistrusted in the US about as much as Muslims are, but there is plenty of bad blood between them. Also we shouldn't forget that there are plenty of Muslims who hate atheists in the same way!
You might hope that oppression and suffering would make people sympathetic to others, but it doesn't work that way so much. Sure, it works if they are suffering for the same reason - I am sure you would find that gay people are very sympathetic towards victims of anti gay bigotry, for example, but even then there are exceptions.
It would be great if everyone could develop empathy for others who have suffered, and that all it took was suffering oneself to bring out that empathy.
But that isn't how the world is. People's empathy for others is trainable, to some extent, and genetic, to some extent, but it doesn't just materialize the first time you have something terrible happen to you.
Which I think is an important facet of intersectional feminism that we ought not to forget. You don't understand the way somebody else suffers just because you have suffered yourself. Being a person of colour is a different thing from being gay in this way, and being a gay person of colour is another entirely different experience, not necessarily derivable from understanding the two things separately.
So we all need to keep our minds open and accept that though we understand how our lives are hard, that doesn't automatically mean we understand how other people's lives are hard. This is true for everyone, and the learning process to try to understand others takes time and effort.