"The Hive" © DigitalBlasphemy.com
If the theology has no problem with science, then there are not limits imposed by theology. There will still be limits imposed by culture or physiology - such things will help affect the direction technological experimentation and exploration takes. But it won't have theological pressure.
If the theology has a problem with science, then there will be limits imposed. On our own Earth there are religious groups that demand that science bend to particular people's interpretations of scriptures. Such demands dictate what is studied, and what isn't. It dictates how data is interpreted. It dictates how it is used. It has a strong influence on the technology.
Others demand that life should be lead as simply as possible, so as to free believers to concentrate more on spiritual development. For them, technological development is not encouraged at all or maybe in only certain niches - medical or maybe for some the technology that helps the religion to spread to others (communication technology, for instance). So, unless they feel OK about developing communication technology, and develop a wish to spread their message to the cosmos, sentient beings whose theology demands a simple life, we may not be able to detect from afar their existence, and to communicate with them.
And, of course, if their world has differing theologies, competing theologies, the effects on technology would be "all over the map." If they devolve into war over these differences, then the effect would be a delay on certain technologies (and an possible encouragement to develop others - types suited for conflict).
Finally, to end this preliminary speculative discussion, some of concerns about contacting aliens center largely around their type of society and theology. Are they interested only in conquering others? Would they treat us as backward barbarians or primitives who have a primitive (and wrong - to them - religion) who must be forcibly saved?