Old earth creationists often assert that their views are distinct to theistic evolutionists, and the better interpretation of Genesis, than proposals of young earthers. Is old earth creationism not a mere attempt to accommodate Genesis into mainstream science? and to make it more " tasteful"? If that is the case, should we really care that much about what science asserts today - faced the fact that tomorrow, their assertions can ( and do ) change?
Donald Campfield Otangelo, you've posted something of a six-chamber/double-barrel topic, so as an OEC myself I'll try to answer your two questions carefully. Even before that, let me state that not all OECs hold the same models or have exactly the same understanding of the early chapters of Genesis as each other. And there may well be other OECs who would disagree with portions of my answers here.
QUESTION 1: 'Is OEC not a mere attempt to accommodate Genesis into mainstream science?'
ANSWER: No, it's not an accommodation at all. "Accommodate" to me denotes/connotes fudging things—dismissing, downplaying, or papering over differences—in order to make one idea or model appear to get along with another which is contrary to it. Instead, the OEC work that I know myself is an attempt to compare the data of scripture—as interpreted by the best Bible scholarship we can muster—with the data of nature—as interpreted by the best scientific theorizing we can muster—in order to see where they apparently agree and disagree; and then, provided it is possible to do so WITHOUT fudging either data-set, to construct a harmonization which adequately explains both data-sets and which resolves the apparent disagreement. The premises behind this harmonization approach are that: (1) God's Word, correctly understood, does not lie to us; and (2) God's natural world, correctly understood, does not lie to us either.
QUESTION 2: "…should we really care that much about what science asserts today—faced [with] the fact that tomorrow, their assertions can (and do) change?"
ANSWER: Let me first answer that question with another: Should we really care what THEOLOGY asserts today—faced with the fact that, tomorrow, the assertions of theologians can (and do) change?"
By asking that reciprocal question, I'm not trying to be coy or evasive. Theology ALSO changes over time, and sometimes quickly (e.g., the personal theology of an individual), but it also changes from place to place and from religious group to religious group, even when everyone is reading the very same Bible and when all agree it is the only/final source for their theology. Consider these theological disparities:
•Pre-, Mid-, and Post-trib
•Pre-, Post-, and A-mil
•Dunkers/Dippers vs. Pourers vs. Drippers
•Dispensationalists vs. Covenant Theology
•Cessationists vs. Continuationists
•Preterists vs. Futurists vs. Historicists vs. Idealists
•Perfectionists vs. Progressive Sanctificationists
•Arminians vs. Calvinists
•Local church autonomists vs. Denominationalists
•Dichotomists vs. Trichotomists
•Trinitarians vs. Unitarian Modalists
•Soul Creationists vs. Traducianists
•Original Sin Advocates vs. Pelagianism
•Justification by faith apart from works vs. Justification by both faith and works
•Seventh Day Sabbath vs. First Day Lord's Day
•Antinomians vs. Legalists
Most of that list is secondary doctrines which genuine Christians can differ on and still remain Christian. At least one—justification—is not.
Now for the rest of my answer: YES, I think we should care about what science asserts today, and that we should care about it approximately as much as we also care about our core- and secondary-doctrine theology. (Why so much care for science too? Because, correctly practiced, it discovers TRUTH, and truth is both essential and useful.) Both science and theology can change, but the most well-established models in both disciplines which have persisted as they continued to explain newly acquired data well over many decades are less likely to be totally overthrown than are more recent and/or data-poor models. I don't think the careful study done by genuine scientists and genuine Christians alike with respect to fundamental truth will cause us to find that our newest data will one day suddenly require us to change our views and to think, for example, that light does not really exist or that Christ was not God incarnate. (There are some pseudo-scientific people and heretics who may think those things, but the data/evidence behind their contrary views contradicts, rather than supports, them.)
Granted, there are some long-established scientific theories which are widely held and defended (e.g., macroevolution) which many Christians cannot agree with, myself included, but because God's natural world does not lie to us these falter in explanatory power over time due to the acquisition of new data. The OECs I know personally have given public lectures detailing what they considered to be insurmountable scientific problems for macroevolution and they gave their presentations without needing or attempting to appeal to scripture or theology at all. All humans are capable of resisting change and of supporting personal agendas contrary to truth, but as long as science remains faithful to its own methodology, it will continue to be self-correcting over time.