I will try to resist this reply: that depends on what you mean by "religious" and "moral." But definitions do matter, and I will not be able to avoid appealing to definitions.
If you have a very broad definition of "religious" according to which being religious involves reverence, caring about what is sacred, being consistent (as when someone might say of an athlete that "she works-out religiouslyl") and if "morality" includes such elements, then, yes, there is an important (at least) intersection between being religious and being moral.
But if by "religious" one means that one adheres to religious traditions such as Hinduism, Buddhism, Judaism, Christianity, Islam.... then most philosophers have not thought that being religious is essential for being moral. In fact, many religious thinkers (theologians or sages) have insisted that morality (both the awareness of what is moral and the ability to live a moral life) is available for persons in general independent of one's religious beliefs and practices. There are various nuances, however, that I address below. Sorry if this reply might appear pedantic, when you probably are hoping for a 'yes' or 'no' response.
Many religious thinkers believe that religion involves far more than "morality" --the worship of God, for example, which is sometimes described as a duty but often portrayed as a great, transcendent experience that goes beyond the realm of morality --just as, on a minor scale, the pursuit of something aesthetic (beauty in the arts) might involve matters that extend beyond (without being in conflict with) morality and ethics. It would be hard to put the greatness of Beethoven's Ode to Joy in narrowly moral / ethical terms.
I suggest that three of the many interesting, debated questions that bear on your question concern (1) whether acknowledging morality as an objective, binding code that calls for (or demands) our allegiance requires a religiously oriented worldview; (2) the extent that religion itself can be reduced to morality and (3) the extent to which religion can either enhance or conflict with moral beliefs and practice (as captured, for example, from a secular point of view).
On the first point, you might find the work of George Mavrodes interesting or challenging. He proposes that an acknowledgement of objective morality requires viewing the world in teleological (purposive or, in his case, theistic terms). Probably the leading advocate for that position today is C. Stephen Evans. On the second point, Kant would be your key reference point. Scholarship on Kant is divided and complex, but more often than not he is seen as a key promoter of the view that at the very heart of Christianity, and all religions when properly purified through philosophical criticism, is ethics. In terms of the third category, perhaps there is no more provocative philosopher for you to engage than Kierkegaard in his dramatic, extraordinary work: Either/Or.
For my own views, check out A beginner's guide: philosophy of religion.