What beliefs would we consider reasonable for a self proclaimed Christian to hold?

[drfuzzy]

Time.  Measured by our awareness as related to the earth's rotation.  So?  Time has no bearing on the existence or non-existence of any deities, and certainly provides no proof of the existence of such creatures.  And sure, we can say a lot about "what's lost to time" (lol) whole disciplines are built around it.  Time was once proposed as a 4th dimension but that was 100 years ago.  Here is a good article on the subject. 
  https://phys.org/news/2012-04-physicists...space.html     
“With clocks we measure the numerical order of motion in 3D space,” Sorli told Phys.org. “Time is 'separated' from space in a sense that time is not a fourth dimension of space. Instead, time as a numerical order of change exists in a 3D space. Our model on space and time is founded on measurement and corresponds better to physical reality.”

don't be dense.

If side deity was reported to walk among us 2000 years ago (a measure of time outside the scope of 'science') then science is restricted by time however you want to classify it.

Say . . . what?  Yeah, maybe I am dense.  That made absolutely NO sense.
A "deity", according to some books of fables, supposedly walked on the planet 2000 years ago.  We understand 2000 years very well.  That's time.  It's a numerical measure of the earth's rotation.  Yes, science is restricted by time.  Every creature, every plant, the earth itself, the solar system, is measured by time.

This does not make time a 4th dimension, it is a measurement only.  And that measurement provides absolutely no data applicable to the existence of any deity.