The spacing of the contracts on an RJ45 is 1mm, so when you see the 8 wire holes all in a row like the one you link to you know that will only fit wires with an insulated diameter of no more than 1mm. The diameter of 24 AWG wires with insulation is generally at or just below 1mm so those should fit in that connector. The diameter of 23 AWG wires with insulation almost always exceeds 1mm by a bit, however, so those won’t fit (easily) in those holes. You instead need to find a connector that has the holes offset up-down-up-down so the larger conductors can be centered over the connector pins.

Almost all solid conductor cat5 and cat5e cable has 24 AWG wires, but most cat6 and cat6a cables claim to have 23 AWG conductors and, if they actually are that size, need connectors with the offset holes. Unfortunately, sometimes “23 AWG” is a lie and the actual conductor diameter is closer to 24 AWG, so the connectors with the straight-across holes sometimes fit on cat6. The only real way to know which connectors are best is to measure the actual diameter of the wires you are installing them on to see if they exceed 1mm.