If, hypothetically, there was to be an experiment that would look for solar activity induced increases in infrared radiation on the International Space Station, would the infrared radiation produced on Earth or from other sources (Cosmic Background Radiation) make the data hard to determine?
In fact the ESA observatory SOLAR has been monitoring the Sun activity from the ISS Columbus Laboratory since 2008. In particular the SOVIM science instrument is in charge to monitor the infrared radiation. Further infrared radiation sources can be handled provided they are well known.
As a first approach:
total amount of power used on Earth: 150 TWh/year. Pretty much all of this ends up as heat, so it's a decent proxy for amount of IR produced.
total amount of solar energy received on Earth: 250 W/m$^2$ times 510 million km$^2$ is 1.275 EW, or 1.11 ZWh/y, or 2 million times as much.
So human production is only a factor if you want to measure to an accuracy of 0.05% or better.
The infrared coming from the Earth, or activities on the International Space Station, won't interfere with an instrument intended to observe infrared light produced by the Sun. The Sun's infrared output is primarily in wavelengths shorter than 1.75 microns. Thermal infrared is at wavelengths longer than 3 microns.
With regard to the CMBR, there's no overlap whatsoever between those long radio waves and the short near infrared produced by the Sun.
The James Webb Telescope will have instruments that look at wavelengths as long as 28.6 microns. That will require extensive cooling, but the Webb isn't intended as a solar observatory.