Is the Statements "Science has been Wrong Before" and "Truth is Subjective none sequitors?

Most commonly used statements I see when somebody's claims are pushed against the wall and in a finally last stand pop one of these babies out. 

Here is a quote from RationalWiki that refutes the “science was wrong before” claim:

“Usually (or at least often) "science was wrong before" is used to defend the existence of a disproven phenomenon — alternative medicine, perpetual motion, crank theories of everything, faster-than-light travel… the list is really endless for where this has been applied before. The usual examples of science being wrong (like the geocentric worldview that "science" used to hold) were theories that were in no way disprovable at the time, much in the way that string theory cannot be readily disproved at this time. Many alternative medical practices, on the other hand, have been carefully shown to be utterly ineffective in one study after another — no additional information will suddenly contradict these results. When used like this, the "science was wrong before" trope is effectively like suggesting that our observations that gravity is an attractive force are wrong, because one day in the future we might just see something go floating up instead of falling down, and therefore homeopathy works.

So while it is true that several believed-to-be-true theories turned out to be wrong, that doesn't mean that theories that have already been proven wrong might suddenly turn out to be right.“

Scientists have been wrong before. They've also been right before, so based on the statement alone, there's no more reason to reject what scientists are saying than to accept it. In other words, "science has been wrong before" is meaningless.

When used to reject a scientific claim this is a non sequitur, yes.

"Truth" isn't subjective, I'm afraid. This is just incorrect.

To say, "science has been wrong before" kind of misrepresents what science is and does. Science is not about being right or wrong, its a methodology and as long as the methodology is followed then the science is being done right, even if it gets something wrong. For example, hypothesis are formed primarily to be falsified. So in science things are shown to be "wrong" more often than they are shown to be "right." And in fact, science being "wrong" is what makes science so strong as it evolves to get better and better accuracy as new data comes in and as more things are falsified. 

There can be some wiggle room for saying Truth is subjective. For example, facts are not and can not be subjective, but truth being a story that resonates with someones truth has some wiggle room. Plus, there are other definitions of truth such as "this is my truth" etc. There are four types of truth; objective, normative, subjective and complex truth. So a possible equivocation fallacy going on there as well. 

"Science has been Wrong Before"...

Well, duh, yeah, scientific methodology encourages, expects, and even demands falsification. If a hypothesis doesn't hold up to scientific scrutiny it is dismissed until someone can replicate it or shows that it works more often than not. 

So, science is wrong most of the time i.e. until it's not.  The leading claim is not a fallacy, because it's not really false. But it is more of a thought-terminating cliché.

Appeal to possibility is what they are doing here.  Just because they can prove the science could be wrong (because it was in the past) does not mean it is.