Reasonably conservative ex academic here. I don't think facts are particularly biased either way, but if anything I'd say that in today's world reality has a distinctly right leaning bias, mainly owing to how extreme left wing thinking has gotten relative to facts that are mostly the same.

You mentioned global warming and the earth's age, and you are correct on both counts, but most conservatives know these things. The core argument you should be having here is about human nature, because that's primarily where conservative and liberal ideology differ. Conservatives and liberals tend to fall on opposite sites of issues like nature vs. nurture, exceptionally vs. equality, competition vs.redistribution, etc. These go hand in hand with policy suggestions in the real world. If success is primarily earned and income comes from providing value, then maybe we shouldn't tax so much. If we're all just products of circumstance, then statistical disadvantages faced by minority groups might best be solved by collective intervention.

Here are some facts that I think have a conservative bias.

• IQ is the single best predictor for financial success. It's about as heritable as income and many results tying the success of parents to their children can be explained this way.
• America actually is the "land of opportunity" in many ways. It's the single best country to immigrate to if you want to maximize the likelihood of you or your children being millionaires, and it has one of the highest income mobility measures in the world in absolute terms.
• Gun ownership isn't a great predictor of gun violence on the state or county level. Poverty is a good predictor, but the best one is the relative size of the black population.
• There are 30 countries where the average IQ is lower than the threshold for being diagnosed with a developmental disability.
• Children in two parent households have the best life outcomes on average. The lowest rates of divorce happen in first marriages between people of similar economic and ethnic backgrounds. Fewer prior sexual partners is also predictive of a lasting marriage.
• Several vaccines were created for H1N1, one of which was Pandemrix. This vaccine caused narcolepsy in many otherwise healthy individuals who were not at risk from the virus. Some countries continued administering the vaccine even after warnings came out, and in one tragic case a healthy nurse committed suicide after being forced to take the vaccine for work. The best vaccine is the best vaccine, not whichever one is available first.
• You've heard of the nail salon shootings in Atlanta. Several days later there was an Islamic terror attack in Colorado that claimed more victims.
• Intimate partner violence is equally prevalent among men and women, and is usually reciprocal. Entire fields of study have been dedicated to interpreting this data in a way that paints men as primary abusers.
• The recent uptick in anti Asian hate crimes in NYC is entirely explained by the actions of African American perpetrators.
• US billionaires have a lot of money, but even if we took all of it today we would only be able to fund the country's budget for a year.

I could go on or debate these in more detail, but you get the point. These facts have a distinct conservative feel to them, at least in my opinion. Mostly these lie in the social sciences, where ability to publish is based both on collecting real world data, but also on interpreting it and creating a narrative that's in line with other research. Bias can be introduced in selecting questions to ask, choosing what data to publish, and in deciding what kind of analysis to perform. During my time in academia I met a lot of people in the social sciences and humanities who identify as being extremely left wing, I can't see how this wouldn't affect their choices in these areas. If I stayed and worked in one of those fields, I'm sure my work would have had a conservative bias as well, but who knows? I graduated in STEM and went to industry.