After the Trump State Department, led by former Tea-Partying House Republican turned somewhat-pathetic diplomatic placeholder Mike Pompeo, refused worldwide U.S. embassy requests to fly the LGBTQ pride flag from embassy flagpoles, some diplomats worked around the ban by instead displaying the flags everywhere besides those flagpoles. Naturally, Vice President and Bag of Highly Processed Pork Fat Turned Into A Real Boy Mike Pence would be asked to weigh in on this latest administration poke at LGBTQ Americans. And naturally, he would voice his full support for Pompeo's refusal.
“As the president said on the night we were elected, we’re proud to be able to serve every American,” Pence said. “We both feel that way very passionately, but when it comes to the American flagpole, and American embassies, and capitals around the world, one American flag flies.”
Say what you want about Mike Pence, but the man has spent a lot of time thinking about flagpoles. Too much time, honestly.
It's not necessarily clear whether Secretary of State Pompeo did this entirely on his own or if it came down as White House edict, mainly because it's never quite clear whether Pompeo has been given the authority to do anything without an accompanying White House edict. Team Trump has been persistent in undercutting LGBTQ rights anywhere it can unilaterally do so, making a special target of the diplomatic community.
Mike Pence himself is notorious for his career of deeply anti-gay declarations and stances, and has been suspected of being a primary force pushing for the moves that presidential "advisers" Jared Kushner and Ivanka Trump have given up even pretending to be privately concerned about. Long before joining Trump's team, Pence was an advocate for "religious freedom" laws permitting discrimination against gay Americans who warned that recognizing same-sex marriages would cause "societal collapse." His campaign website featured a "Pence Agenda" that called homosexuality "incompatible with military service because the presence of homosexuals in the ranks weakens unit cohesion" and which demanded that federal HIV prevention measures exclude funding for organizations that "encourage" homosexuality.
So no, it's not at all surprising that Mike Pence doesn't believe pride flags belong on flagpoles. That's his thing.