Is it disrespectful to turn my back to the Quran?

Intention is what counts

The Prophet ﷺ said actions are judged by intentions (Sahih al-Bukhari 1). Walking past a bookshelf, sitting in a room where a Quran sits behind you, or turning to talk to someone isn't an act of disrespect. Nobody intends anything bad by it, and Islam doesn't ask you to keep track of where every copy is at every moment.

What happens in mosques

Look around any mosque in Europe or the USA. Quran shelves are often on the back wall, and the whole congregation prays with their backs to them. The imam faces the qibla with his back to the people, and the prayer rows sit wherever there's space. Nobody considers this a problem. That shows how scholars and ordinary Muslims understand the issue: having your back to the Quran is not, in itself, disrespect.

Showing honour where you can

Honouring the Quran is part of faith:

Many scholars list small courtesies as part of that honour:

• Don't deliberately turn your back or stretch your feet toward it in a way that looks dismissive, if you can easily avoid it.
• Keep it in a clean, raised place rather than on the floor. See Can I put the Quran on the floor?
• Don't place other things on top of it.
• Store it somewhere respectful at home. See Where should I keep the Quran at home?

These are manners, not strict rules. Scholars generally treat them as recommended rather than obligatory.

Don't let it make you anxious

Converts sometimes become very worried about "doing it wrong" with the mushaf. Allah knows what is in your heart. Someone who loves the Quran and reads it with care is honouring it, even if a copy ends up behind them sometimes. Some people kiss the mushaf as a sign of love, and others don't; both are fine. See Can I kiss the Quran?