If one is false, then all are false.

FYI: I did some further research and discovered this interesting and somewhat obsolete legal philosophy.

Falsus in uno, falsus in omnibus is a Latin phrase meaning "false in one thing, false in everything."[2] At common law, it is the legal principle that a witness who testifies falsely about one matter is not credible to testify about any matter.[3] Although many common law jurisdictions have rejected a categorical application of the rule, the doctrine has survived in some American courts.[4]

Hasty Generalization Fallacy

Fallacy of Composition

Sweeping Generalization Fallacy

Those are the three that popped up in my mind initially.

As much as I would like to say the person is just a moron (i.e., this is a more of a matter of ignorance), I want to apply the most charitable interpretation here, simply because I think someone saying something so idiotic is improbable. It could be the case that this person denies the core of scientific methodology— consistency and universal laws. If it were the case that this foundation is false, then anything built on that foundation is also be false (kind of like building a house with cement that deteriorates after a year... if one house goes down, all the others in the neighborhood that used that same cement will almost certainly follow). In fact, this is how many young earth creationists justify their position: they acknowledge the speed of light, but suggest that it was different in the past (not consistent). They acknowledge radiometric decay but again, will deny that it was always that way. In other words, they reject a core observation in the universe not because of any evidence to the contrary, but because, in their belief system, it just can't be right.

Hmmm, let's see: false premise, false equivalency, non-sequitur and wraps up with a part-to-whole fallacy (“if one theory is false, all of them are.” ) Obviously the claimant misunderstands the distinction between scientific theory and the general term "theory". Natural Selection is proven science and a fact - not speculation or belief. The idea that organisms can evolve by micro and macroevolution is a fact.

Likewise, Gravity is Physical Law and among The Standard Model of Particles along with Electromagnetism, Weak and Strong Nuclear forces, etc.

The Christian flat earther wrongly equates evolutionary biology with physics and cosmology even though they are possibly two (three) distinct scientific disciplines. AS Dr. Bo explained, the Christian's simple-minded argument is really an attempt to discredit scientific methodology more than anything else. Fortunately, much of that very methodology is about proving weak and implausible beliefs like intelligent design, flat-eartherism, and religious superstition as false, and that is not theory, but a historical fact.