Are the present day Jews and Christians considered as disbelievers?

Are the present day Jews and Christians considered as disbelievers? Some people say that the messenger of Allah called them people of the book. If we call them disbelievers, will that have any effect on our Iman?

الجوابُ حامِدا ًو مُصلیِّا ً

The Jews and Christians are disbelievers because they did not believe in Muhammadﷺ as the messenger of Allah, and the Quran as the book of Allah. It is permissible to call them disbelievers, and doing such will not affect one's Iman in any way. Furthermore, they have also been called disbelievers in many verses of the Quran and Ahadith.
And Allah knows best.

مأخَذُ الفَتوی

قال اللہ تعالیٰ: {يَاأَهْلَ الْكِتَابِ لِمَ تَكْفُرُونَ بِآيَاتِ اللَّهِ وَأَنْتُمْ تَشْهَدُونَ} [آل عمران: 70]
وفی أحکام القرآن: عن أبي هريرة قال: قال رسول الله صلى الله عليه وسلم: «لا تصافحوا اليهود والنصارى» فہذا کلہ من ۔۔۔ البس اللہ الکفار بکفرھم اھ (۳/۹۹)
وفی الدر المختار: والكفر لغة: الستر. وشرعا: تكذيبه - صلى الله عليه وسلم - في شيء مما جاء به من الدين ضرورة اھ(4/ 223)