Is Yoga a modern religion?

Yes,

Yoga is not merely a meditation style it is part of Hinduism,the oldest religion in the world. I am a Indian Catholic and I don’t practice Yoga for the same reason.

The ultimate goal of Yoga is moksha (liberation in Hinduism and Hindu philosophy), although the exact definition of what form this takes depends on the philosophical or theological system with which it is conjugated.

According to Jacobsen, "Yoga has five principal meanings:

1. Yoga, as a disciplined method for attaining a goal;
2. Yoga, as techniques of controlling the body and the mind;
3. Yoga, as a name of one of the schools or systems of philosophy (darśana);
4. Yoga, in connection with other words, such as "hatha-, mantra-, and laya-," referring to traditions specialising in particular techniques of yoga;
5. Yoga, as the goal of Yoga practice.

Classical Yoga

Yoga is considered as a philosophical school in Hinduism.

Yoga, is one of the six āstika schools of Hinduism (those which accept the Vedas as source of knowledge).

Due to the influence of Vivekananda, the Yoga Sutras of Patanjali are nowadays considered as the foundational scripture of classical yoga, a status which it only acquired in the 20th century.

Before the twentieth century, other works were considered as the most central works, such as the Bhagavad Gita and the Yoga Vasistha, while Tantric Yoga and Hatha Yoga prevailed over Ashtanga Yoga.

Ashtanga Yoga

Yoga as described in the Yoga Sutras of Patanjali refers to Ashtanga Yoga.

The Yoga Sutras of Patanjali is considered as a central text of the Yoga school of Hindu philosophy,

It is often called "Rāja yoga", "yoga of the kings," a term which originally referred to the ultimate, royal goal of yoga, which is usually samadhi, But was popularised by Vivekananda as the common name for Ashtanga Yoga.