Interesting points. Before I dive into my thoughts, I'll preface by saying that I don't believe all facts are relative. However, my idea of objective fact is more limited.

First, I would like to present a few definitions for Truth.
A verified or indisputable fact, proposition, principle, or the like: mathematical truths.

1. actuality or actual existence.
2. an obvious or accepted fact; truism; platitude.
3. accuracy, as of position or adjustment.
4. http://dictionary.reference.com/browse/truth

To 1 I say yes, absolutely. That is one thing Descartes and I agree on. 2, generally yes but these are usually "so what" kinds of truth. 3 would be true in the same way mathematical statements are true. Which brings us to:

It is universally accepted that the sky is blue, the sun is bright, and 1+1=2. These are objective truths that are not a matter of opinion.

and

There are laws in this world that are indisputable. Gravity exists, you can empirically experience it. It is indisputable that it exists.

Except for 1+1=2, these are empirical observations. We see the sky is blue and sun is bright, but what if this world is an illusion (the matrix if you must)? In that case there is really no sky or sun and the colors are arbitrary and may truly be different to everyone in the simulation depending on your configuration. Add to that, "bright" is absolutely a relative phenomenon. The sun is the brightest thing in the solar system, but there are surely stars in the universe that would over power our sun many times over. "blue," or any color for that matter, is a subjective experience. Don't believe me? Ask my wife, who apparently sees several distinct shades of color that do not exist to me.

Laws of the universe like gravity? It's indisputable that it exists? See the simulation hypothesis above. There is a deep epistemology argument lurking here that is beyond the scope of this discussion, but we can say "indisputable" is not true.

1+1=2? Yes, but this is true by definition. However, it is interesting to note that the symbols are arbitrary and should not be confused with the actual concepts "one" and "two". (Note, this probably is a bit of sophistry, but a fun bit). Take this statement: 1 + 1 = 10. True or false? Depends on the base you are using(2). 1 + 9 = 10? Wrong, it's A (16).

Obviously, denying facts like gravity, color, and arithmetic is highly unproductive for day to day life. My view of facts is that the definition of a fact is context dependent. Are we talking pure metaphysics and epistemology? In that case, the only fact I'll admit is my immediate experience (how's that for skepticism!). Are we discussing politics? There is a whole host of things about the world and basic human existence that we must accept as given (similar to axioms in mathematics) to have a political discussion.

When we enter into a discussion, we must have a basic level of agreement on how the world works for anything we say to make sense. Breakdowns occur where people do not agree on what facts can be accepted as unquestionably true. For example, many believe the identity of sex and gender is an objective fact and arguing against this type of person with statements like "gender is taught and a product of culture(aka "relative")" is like speaking in tongues. Is either person "wrong" in this case? I would be hesitant to label objective truth in an argument of this kind.

What is objectively true, is that if you have made it to the end of this rant, you have more patience than 99% of the human population.