To my feeble understanding.
Karma-yoga is mixed Bhakti, where the person serves God for some purpose (i.e a car, house, a 'lady'). But the person does pray to God, (eventually) coming to higher understandings. That these material aquesziations are not the real purpose. i.e Praying to God for material desires (demi-Gods) is Karma-yoga. Islam for example is considered Karma-yoga, but mixed with Jnana possibly. Christianity is possibly the same? Karma-yoga and Jnana-yoga. Although they do explain Bhakti-yoga as well.
We have to choose one or the other, all religions come under either one of the catergories, so everybody has chance to serve God. For example in Islam they desire heavenly happiness (material desire), but they want to serve Allah as well (so its mixed Bhakti (Karma-yoga).
Christians desire to serve Lord Jesus and Jehovah, but they too have desire for heavenly happiness (Karma-yoga). Possibly both mixing with Jnana-yoga. But this desire makes us want to serve, and it purifes us eventually. So they are good for the soul.
Eventually though Bhakti-yoga (Direct Service to God without any adultaration (pure bhakti), total surrender is recommened.
Also Karma-yoga, as Impersonal realizations (Jnana), Demi-God worshippers have Personal (?), everybody wants something different.
In India people worship mosly Shiva, and Ganesha and Hanuman. But mosly because of 'practise' They always worship Janamastami Celebrations (i watched one yesterday with my cousins in India, was amazing). So everybody is trying to serve God, and everybody is judged individually.
When I went to Islamic forum, most Muslims are very open, but mosly they are just starting out (like us), so it's not good to disturb I found out. Same with Christians, I found better to not disturb somebodies creeper.
Krishna has given so many paths (His all merciful!!!). So people eventually come to Him.