This depends on what it means to “believe in America”. If it means believing that all other Americans are non-violent, then the meme makes perfect sense. However, such a belief would be delusional.
If believing in America means believing in the ideals expressed by the Declaration of Independence and the Constitution, then arming oneself makes a lot more sense. Is it against American values to believe that under certain circumstances rebellion against the government is justified? Let me quote a famous American document (emphasis mine):
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.–That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, —That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
Does this justify rebellion against the current government? We can argue, but I am very clearly in the no camp. Revolution is almost always a bad idea, as even the declaration says:
Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed.
However, it means that rebellion is justified under certain conditions. Therefore, being armed lest such conditions happen and you won’t have the means to rebel is consistent with American values or “belief in America”.