Well, the only other group to face similar persecution from the Romans were the Jews. And Christians, for the most part, were for a long time considered by the Romans (and considered themselves) as a sect of Judaism. What set Christians/Jews apart from other Graeco-Roman cults was the idea of exclusivity; that you could only "believe in" and worship God, and that all other "gods" were either non-existent or demons. Prior to Christianity, "religion" wasn't really a concept. The gods you worshipped were tied to your ethnicity. While there are examples of gentiles converting to Judaism, or Jews disavowing their religion for Graeco-Roman paganism, "conversion" doesn't really become a tangible practice until Christianity comes along, when Christians basically present their sect as a version of Judaism open to all gentiles.

Even though this requirement of exclusivity was the source of persecution for Christians, one could also argue that it contributed to Christianity's success. This policy of renouncing one's previous gods upon joining meant that as Christianity grew, those competing sects of Graeco-Roman paganisms shrank.

So, there really weren't any other "religions" in the modern sense. But there were a ton of non-exclusive cults throughout the empire. Mystery cults like those to Demeter, Isis, Sarapis, Dionysus, and Mithras were quite popular. There were also other polytheistic religions tied to various other ethnicities, like the pantheons of the Palmyrenes, or the Nabataeans. There were even cults tied to charismatic leaders, like the one that developed around Alexander of Abonuteichos (as described in Lucian's Alexander the False Prophet). But again, since this is Graeco-Roman paganism we're talking about, the cult was non-exclusive, meaning one was welcome to worship Alexander alongside the rest of the traditional Graeco-Roman pantheon.

Some good sources to look at for mystery cults might be:

Walter Burkert's Ancient Mystery Cults

Marvin Meyer's The Ancient Mysteries

and Jan Bremmer's Initiation into the Mysteries of the Ancient World (available as a free ebook here).

Regarding the separation of Christianity from Judaism, you might consider checking out Daniel Boyarin's Border Lines: The Partition of Judaeo-Christianity

and Douglas Boin's Coming out Christian in the Roman World: How the Followers of Jesus Made a Place in Caesar’s Empire

And also, regarding how the category of religion was basically invented by post-Enlightenment Christians: Brent Nongbri's Before Religion: A History of A Modern Concept

Unfortunately, there aren't really any good recent, easily accessible books on non-Graeco-Roman paganisms, but Javier Teixidor's The Pantheon of Palmyra and Peter Alpass' The Religious Life of Nabataea are good scholarly surveys of those two cultures.

Hope that answers your question.