Thank you for your comment. I'd like to speak into your concern.

While I think it's valid for a Catholic to not supporting any social/political movement or party that isn't fully in line with Church teaching, I do think that severely limits Catholic participation in society. I think it's better for Catholics to be involved in things that are less than the ideal in order to plant seeds for positive change and steer the movement in a direction more in line with justice and truth. I believe I'm echoing what the US bishops in their voting guide:

"The Catholic call to faithful citizenship affirms the importance of political participation and insists that public service is a worthy vocation. As citizens, we should be guided more by our moral convictions than by our attachment to a political party or interest group. When necessary, our participation should help transform the party to which we belong; we should not let the party transform us in such a way that we neglect or deny fundamental moral truths or approve intrinsically evil acts. We are called to bring together our principles and our political choices, our values and our votes, to help build a civilization of truth and love."

Also, there are positive aspects of Pride like working for civil rights for LGBTQ folks, especially access to housing and employment, and decriminalizing homosexuality around the world. There was an interview a few years ago with Fr. Philip Bochanski, the executive director of Courage, who said, “Catholics should keep in mind that Pride events ‘were originally meant to draw attention to unjust discrimination and harsh and sometimes even violent treatment against people because of their sexual attractions and their understanding of their sexual identity.’”

So I think a Catholic can absolutely fly a Pride flag in solidarity with those fighting for civil rights for LGBTQ folks.

Those are my thoughts. I'd love to hear your perspective.