My cacti are going very pale. I've been putting them out in nice bright light to try and combat this but it seems to make it worse. Are they burning/too hot?

To me it looks like a substrate problem. If they were burning they would be red/brown. It may be that they are lacking nutrients. I suspect, by the look of that substrate, that they are having trouble getting their roots through that soil. It looks very compacted. I've had this issue in the past and I had to start using a different substrate. Transplanting them now would just harm them though. In the future use a better substrate that doesn't get so compacted like that and that is "fluffier" What kind of a mix is that? And also, it's kind of hard to see the color from these pictures, but they don't look too bad off to me. I do notice that some of them aren't standing upright which could be an issue of the soil being too hard to penetrate and compact. Therefore the roots aren't doing too well and keeping the seedlings upright.

20/40/40 - perlite/sand/garden soil :/
I think you are right. The soil is very compact.
What do you suggest as a course of action?

some types of sand are very bad for growing cactus (or nearly any plant that can't tolerate waterlogged roots) - they just get waterlogged and totally choke the roots air supply.

I experimented with a bag of "horticultural sand" with extremely poor results and never used sand again. perlite/soil/coir/compost in various combinations works great to grow just about anything. 50/50 perlite/soil is pretty much foolproof for growing trichs.

I think "coarse sand" or "sharp sand" are the ones that drain well, but I never felt compelled to figure out what kind really works because my soil mixes work great already.

I have successfully transplanted seedlings that young. You could also try grafting them.

seedlings do not need strong light at that stage.

agreed
cant tell by the pics but a simple floro light is fine at this stage.

I've transplanted 75 of the seedlings into a new mix which is light and fluffy, and they've already started to recover their rich green color.

Oh the joy

Thanks guys