Does the First Amendment Interfere with the Sixth Amendment?

There's always loopholes to everything. Doesn't matter what it is, it's just a matter of finding them. The first amendment grants people the freedom of speech, with few limitations. All of the limitations are reasonable. Incitement is off limits, along with threats and other harmful things. The sixth amendment grants people the right to a fair trial. This means they will receive an impartial judge, have a speedy trial, right to know who your accusers are, a chance to confront your accusers in court, and the right to a lawyer. There's more that goes into both of those laws, but that is the gist of both of them. So, how can the first amendment interfere with the sixth amendement?

The first amendment allows racist people to be racist, as long as they are not harmful with what they say. This gives the press free reign to flip any story they want into whatever direction they want it to go in by the power of persuasive speech and advertisement. A good example of this would be in the Jogger Case of 1989. In this particular case, there were no DNA traces that led back any of the men accused of the rape of the Central Park jogger. No semen traces, clothing traces, nothing. That alone should've told the judge, jury, and investigation teams to take a step back and realize that they were making a mistake. However, the media placed such a bad name over these boys. People are so easily influenced by the media. it would be foolish of me to think that the judge was impartial in this case, given the outcome, with all of those horrific headlines circulating across the country.

Here's a link for further research:

https://www.law.cornell.edu/constitution/sixth_amendment