Why does current change when adding in an LED?
A bog-standard red LED has a forward drop of about 2 volts at 20 mA so yes, it has a significant impact in what current might flow when the supply voltage is only a few volts: -



So, with 2 volts across it and 20 mA flowing, the perceived resistance is 100 ohms. With 1.9 volts across it, the current is only 5 mA and the perceived resistance has risen to 380 ohms. At only 1.8 volts, the current might be 1 mA and this means it looks like 1800 ohms. Do you see the issue?

For instance, if your supply voltage was only 1 volt then forget it because it won’t overcome the innate forward voltage of the LED and, barely nano amps will flow.

Other LED colours can have significantly higher forward voltages so, what you are trying to achieve depends on the LED type.

So, like the game rock, paper and scissors, the LED dictates current flow at low voltages but, at higher voltages, the series resistor wins.