SARS-CoV-2 spike requires proteolytic processing for viral entry. A polybasic furin-cleavage site (FCS) in spike, and evolution toward an optimized FCS by dominant variants of concern (VOCs), are linked to enhanced infectivity and transmission. Here we show interferon-inducible restriction factors Guanylate-binding proteins (GBP) 2 and 5 interfere with furin-mediated spike cleavage and inhibit the infectivity of early-lineage isolates Wuhan-Hu-1 and VIC. By contrast, VOCs Alpha and Delta escape restriction by GBP2/5 that we map to the spike substitution D614G present in these VOCs. Despite inhibition of spike cleavage, these viruses remained sensitive to plasma membrane IFITM1, but not endosomal IFITM2 and 3, consistent with a preference for TMPRSS2-dependent plasma membrane entry. Strikingly, we find that Omicron is unique among VOCs, being sensitive to restriction factors GBP2/5, and also IFITM1, 2, and 3. Using chimeric spike mutants, we map the Omicron phenotype and show that the S1 domain determines Omicron's sensitivity to GBP2/5, whereas the S2' domain determines its sensitivity to endosomal IFITM2/3 and preferential use of TMPRSS2-independent entry. We propose that evolution of SARS-CoV-2 for the D614G substitution has allowed for escape from GBP restriction factors, but the selective pressures on Omicron for spike changes that mediate antibody escape, and altered tropism, have come at the expense of increased sensitivity to innate immune restriction factors that target virus entry.