Why did critics think that the policies of the Federalists were a threat to the young nation?

The greatest fear of the revolutionaries in the years following the conflict was that the government of the United States would simply turn into an imitation of the British monarchy.  In the 1790s, several things happened under the Presidencies of George Washington and John Adams to further their suspicions.

While it's true that Washington was, for the most part, beloved by both Federalists and antifederalists, that doesn't mean they let him off the hook. In 1794, his Chief Justice, a Federalist named John Jay, was sent to England to negotiate an agreement about our borders with Canada, British troops still present in the Ohio country and freedom of the seas.  Just to be diplomatic, he kissed the Queen's ring when he arrived.  When news reached home, the antifederalists were frothing at the mouth, thinking it was treason to show such subservience to the country we had just won independence from.

An armed rebellion in that same year took place in western Pennsylvania, mostly by farmers who were angry over Hamilton's tax on whiskey.  After a few days of rioting, Washington's army of nearly 13,000 arrived to restore order, except most of the rebellion was over by this time, and it looked an awful lot like something the British would have done, sending in such a large force against their own countrymen.  Grumbling continued.

Then under John Adams in 1798, a federalist Congress passed, and the President signed, the Alien and Sedition Acts which, among other things, forbid open criticism of the government under threat of arrest, a clear violation of the 1st Amendment.  Now the government was trying not only to stifle dissent, but it was clearly aimed at antifederalists unhappy with Adams' government.  They felt the Revolution was slipping away.  Fortunately they were wrong.