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A person dismisses an otherwise valid argument, because some of its proponents support it for the wrong reason.
How is this fallacy called?
EDIT: Here is an example. A person defends the idea that the earth is flat. In an interview he asks several skeptics and each one of them responds "The earth is round because if you dig deep enough you'll reach the other side". The person then shows that this is a circular argument and then concludes that the earth is flat.
The question is vague, so it can be several different things. Generally, dismissing an argument based on who is supporting it is called ad hominem, "attack on an argument made by attacking the character, motive, or other attribute of the person making the argument, rather than attacking the argument directly". It might also be what is more specifically called converse appeal to authority "that must be false, because that's what [infamous expert] says".
However, I am not sure what is meant by "otherwise valid", and "support it for the wrong reason". If their reason for supporting it is part of their argument, and it is wrong, then the argument is at least unsound (has false premises), or perhaps even invalid, if the wrongness affects the reasoning. If proponents who present "partial and weaker (and easier to refute) representation" of the argument are deliberately picked out this would be the selection form of the straw man, which Talisse and Aikin call "weak man", and in extreme forms Drum calls "nut picking", i.e. cherry picking nutty supporters.
EDIT: Based on the added example, this seems closest to the ad ignorantiam, appeal to ignorance, ("ignorance" refers to lack of contrary evidence), concluding that X because presented arguments for not X are all flawed. Of course, it is not necessary that they are flawed specifically due to circular reasoning. The fallacy illicitly shifts the burden of proof to the opponents by asserting one's own position as the default. It is a case of false dilemma, because it excludes the possibility that presented evidence is insufficient to draw a conclusion either way. The proverbial rebuttal is the oft-quoted "the absence of evidence is not the evidence of absence", or in this case, the absence of good arguments to the contrary is not an argument for their absence. In the example another false dilemma appears in the presumption that the Earth is either flat or round.
Bad Reasons, or perhaps Fallacy Fallacy.
The question is not "vague." The answer is a fallacy fallacy - to conclude an argument's conclusion is wrong because the argument commits an informal fallacy and is thus invalid.
If we have only known incorrect arguments to support a conclusion, then we can dismiss the conclusion as "not proven". That's not a fallacy. Incorrect arguments cannot prove the conclusion.
If we have several arguments, of which some are known to be incorrect, and some are correct, then we should ignore all the incorrect ones, look at the arguments that are correct, and check that they prove the conclusion. If they prove the conclusion, then it would be a fallacy to reject it because of the incorrect arguments. (After all, I'm sure we can come up with incorrect arguments for about any correct conclusion).
If we have only known incorrect arguments to support a conclusion, then it is a fallacy to say that the conclusion must be wrong. Incorrect arguments prove nothing. However, if we find correct arguments that the conclusion is incorrect, then we can and must say that the conclusion is wrong.
I think a good example of what the asker means is this: "Global warming is real, because:" - rainbows exist - gawd hugs us closer - sunspots
This seems a reversal of the Jumping to conclusions fallacy
