Is this an example of "Ad Hominem (abusive)"

Allow me to restate this into what I understand you are saying.

You make a point and cite a source as evidence to support that point. The other person does not accept your evidence, claiming the source is not trustworthy. 

It is not a clean Ad Hominem. It could simply be an honest questioning of the source. However, you should be able to make your point using your own explanation. I’m sure you have heard the expression, “I know what I mean, but I can’t explain it.” Whenever you hear that, the speaker does NOT know what he means because language is primarily a tool of thought and secondarily a tool of communication. Therefore, you need to reword your point so the other person understands your point, and then you focus the discussion on the point.

If the person insists on ignoring the point, as you say, you are facing the Fallacy of Diversion (when you have no answer to the topic, you divert the discussion to something more comfortable). Or, the Fallacy of Selective Attention (occurs if one focuses on specific aspects of the argument while ignoring other parts. This usually results in irrelevant rebuttals, straw man fallacy, unnecessarily drawn-out arguments, and a waste of time

If I post an article that contains a statement that I am using to back up a point,

What you mean here is important. Is the "point" a fact or even an argument, or just an opinion/rant/claim? It matters because the opinion/rant/claim from someone not respected is of no value when it comes to "backing up a point." To illustrate, if I argued that all immigrants should stay out of America then told my liberal friend to read an article by Tucker Carlson to back up my point, my liberal friend would be fully justified in saying that "Tucker Carlson is a conservative trash," and refuse to read the article. They are not arguing that because Carlson is trash, then they are right; they are just arguing that because Carlson is trash, they are not going to bother to read the article he wrote.

Now, let's assume that this article you referenced did provide evidence for an argument or facts that proved your point. For the other person to have committed a fallacy, they would have needed to say or strongly imply that because the source is "trash" then what is written in the article is false. Then, it might be more of a genetic fallacy than an ad hominem (abusive) .

Be careful not to let an article or other source do your arguing for you. It should only be used for reference. I am not sure if you did that here, but just pointing it out in case.

One more wrinkle here...  if they are saying or implying that because the source is "trash" that it can't be trusted, then this is not a fallacy; it might be more of a core error with their epistemology if the source is indeed legitimate. If the source is "liberal trash," then there would be no error.

In conclusion, the fallacy is not clear to me from the details given. It is good to get in the habit of asking follow-up questions before accusing one of fallacious reasoning. The conversion might go something like this:

Person 1: Allowing gays to legally marry is far more beneficial to society than harmful. Here is why (all reasons listed and argued here). For more details on this and for the data backing up my arguments, see (source here).

Person 2: Your source is liberal trash.

Person 1: Are you saying because my source is liberal trash, therefore the claims are wrong?

(if yes, see genetic fallacy )

Person 2: No, I am just saying that it can't be trusted.

Person 1: Fair enough, but the source was just backup for my arguments made. Which claims/data/facts are you disputing? Which arguments do you disagree with and most importantly, why?

The goal here is to focus on a specific argument or claim so the conversation can move forward.