One can be a faithful, orthodox, conservative Christian and believe the earth is very old, or at least that it's probably not quite as young as YECs hold. Here are some (scientists):
James Tour
Henry Fritz Schaefer
Hugh Ross
Stephen Meyer
Ian Hutchinson
Don Page
etc

An Old Earth position has not led any of these men to compromise on Adam as humanity's federal head and Christ humanity's savior.

At the moment, and for the past 200 years or so, the YEC position is APPARENTLY at odds with a number of scientific discoveries (rm dating, fossil record, speed of light). These discoveries are absolutely ones which require interpretation.

The consensus among Scientists is that the best interpretation of this conglomeration of evidences is that the earth is probably 4 billion years old or so. This COULD change. Significant errors in dating could be discovered, new digs could provide contravening evidence etc.

Consensus is PROVISIONAL. Nothing in science, however much materialist scientists of a particularly strident variety might shudder at the thought, is settled. Things are more probable then not at a given historic period and given the evidence at hand.

If a Christian believes that this OE interpretation contradicts the deliverances of the Scriptures, this person should say something like, "I believe the Scriptures teach a young earth, here I must disagree with the consensus." This is a principled position to take.

If a Christian believes that Genesis (and the rest of the Scriptures) leaves the age of the earth an open question, he/she has the freedom to either agree with the consensus view (posing as it does no threat to the faith as they say it) or to remain agnostic.

My own position: Genesis leaves the question of the earth's age underdetermined. I do not chafe at the possibility that our earth is billions of years old. It very well could be and I do think the interpretation of these scientific evidences that the earth is old is much stronger

... than the YEC position. I don't believe a YE interpretation is required by the text as it is shot through (in places) with poetic elements. Genesis poses lexical challenges to interpretation that numerous Christians throughout the ages have remarked on(Augustine most famously)

Because I think valid and persuasive arguments can be articulated FROM THE TEXT both that the earth might not be 10,000 years old and could be billions AND that the earth might be 10,000 years old, I don't feel bound by the Scriptures to affirm one or the other.

Striving to maintain a keen awareness of the provisional nature of science in an intellectual climate which has essentially elevated scientists to the heights of the gods is certainly difficult, but this cognizance means that I don't feel bound to affirm what "the science says"

IN SUM: 1. I don't believe the Bible speaks definitively ONE WAY OR THE OTHER to the question of the earth's age.
2. I don't believe Scientists are infallible, and believe their pronouncements on this question could prove mistaken or fatally flawed.
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3. The interpretation of the evidence delivered to us from RM dating, fossil record, relativity, etc, makes more sense given an old earth.
4. I DON'T KNOW HOW OLD THE EARTH IS.