Necessary to use respirator with booth?

I use both, but cheat for quick jobs and paint without the respirator but I shouldn't.  

For Alclad, anything with lacquer thinner. 

Otherwise no, but the fan has a good filter.

How much do you value you lungs? A booth will never get all the particles out. Combined with a resperator you have a high level of protection.

If I had both, I would use both. Certainly with any solvent-based paint as previously mentioned. Also if laying acrylics down heavy.

Unfortunately, all I have is a NIOSH respirator and a big box to shoot into. Not ideal, I know.

Usually, Unless you have a very powerful exhaust fan or are spraying very small volume of paint.  If you can smell the paint you should be using a respirator.

Although I have an effective spray booth, I wear a respirator at all times. I where it whether I am sparaying acrylics, enamels or lacquers. 

No.  Even in winter when I do not exhaust the booth outside.  I find the filter absorbs enough that I get very little vapor outside booth.  I believe most of the odor and vapor comes from the surface of the tiny droplets, and these are caught by the filter.

I wear one when I spray my primer because I can smell it and it makes my sinuses go nuts so the respirator is a must. I don't wear it when spraying my Tamiya acrylics.

I use a 3M 6000 series respirator, it works well and cost about $30-40. It uses replaceable cartridges, about $10, that screen out particulates and vapors. It's recommended for painting and solvents. When it's on I can't smell any of the fumes from paints, lacquer thinner or paint thinner but when I remove it I notice them, even with a booth vented to the outside. There always a lot of debates about what to use and the level of hazard posed by hobby-level painting, but when I see how much stuff accumulated on the booth's filter and the sides of the booth I knew I didn't want that in my body. Unfortunately, with the covid-19 problem all of this stuff is hard to come by. Good Luck!

Ken