All religions have got a set of morals and ethical principles and commend them to the followers as to be part of their lives. Religions do contain certain theological postulates and consequential derivatives. Often these too are based on morals. Though some religions have some notions of reward and punishment for moral life and immoral one respectively, this can be just taken as emphasis of basics.
Since any law, for enforceability has to have an element of deterrence, these religions over-emphasize the aspect of punishment. Sans this too, the social pressure possible to be exerted, by co-religionists, is sufficient enough deterrence.
So, I do not find any dichotomy between religions and morals.
The problem comes only when "we and they" us and them" attitude gets developed vis a vis other schools of theology. Non-realization that own religion is one among several but a dogma that it is 'the religion' and 'the truth' leads to negative tendencies and cause fissures and fragmentation of humanity. Proselytisation though perhaps originating in the good sense of making all to reap the benefit one has 'experienced' degenerates into zeal,mission and frenzy, and leads to forcible approach, and inducements (which in other spheres of life would be called bribery or illegal gratification), are bandied out. "Ends justify means" theory gets developed. Resistance is met with brutality and the nomenclature of 'holy war' (with its equivalent in different languages) is invented, propagated, nurtured,indoctrinated and people get brain-washed.
At this stage all morals, which are inherent in the religion are relegated as impeding elements, in the mission. Then inevitably violence, counter-violence and more repetitions recur. Religion is thus de-valued.
Each one definitely can get his/her morals from one's own conscience. But this does not necessarily postulate that all doctrines handed down to humanity through the ages by great masters ,seers and sages are to be per-se discarded and fresh introspective inquiry alone is to be launched.
The greatest threat to morals does not emanate from religions but by crash consumerism that dictates a theory that standard of life is measurable by acquisition of material wealth. Sharing and compassion, spending only when necessary, saving for sharing the misery of others and several other principles of nobility are not to be sacrificed at the altar of Mammon.(allegorically stated).