“Secularity” is often distinguised as “what is secular” compared with “secularism” which means the promotion or the expansion of secularity. The problem is not what is secular but an expansive meaning to what is secular.
Historically, “secular” meant of an age or of this world (as opposed to the age or world to come) or civil or worldly (as opposed to spiritual or religious). One conclusion is that matters to do with the world before mankind existed should not be considered secular. Just like the age to come, that is a matter for religion. So “secular science” should not concern itself with matters of ultimate origins, nor of a “deep time” that is said to occur before humanity existed.
Since vast ages of time before the advent of man were accepted into science in the 19th century, science is no longer genuinely secular. It has crossed the line into the dimension beyond this age, the age of human life in this world.
Creation science also crosses this line in a different way, following the revelation of the creation week. Those who want a secular science will have to drop deep time or creation and only reference this world, the world of human life.
So a genuinely secular science would be a limited science that could not explain many things such as how humanity got here, how the earth got here, or how starlight got here. It would be a limited science.
It would still be possible for a secular science to be influenced by non-secular perspectives as long as it doesn’t stray beyond its borders. There would be a limited, but level field for science to take place.