Are you pressing after cutting? I spray to fabric with starch, wait for it to almost dry and then dry press. Don't iron too much as in moving the iron. Then carefully fold and cut. Do not iron after cutting except to press the seam.

Take a good look at your fabric's grain before you do anything. Some fabrics can be wound off grain on the bolt.

If it looks off, then tear a strip from selvedge to selvedge which will stay on grain. You can sometimes reblock fabric.

I made quite a few colorblocked shirts using good quilting cotton. You see off grain when you lay out a clothing pattern.
To be fair, it's usually the lower priced cottons that can be off, but if the cheaper cotton is the color and pattern you want, you use it.

I agree that spray and press should be a big help. Another thing I do is to place 3 strips of blue painters masking tape on top of each other 1/4" to the right of the needle. When my material hits the edge of that tape, that gives me an exact 1/4" seam. Good luck

Something else you might want to check - which I got help with myself from the board: is the height of your cutting table correct? Mine was too high and as I cut a strip I was losing control of my ruler. It was suggested that I lower the table surface a bit and make sure I was not standing too far right or left of the ruler. Correcting the table height and squaring my stance has made a HUGE difference in my strip cutting abilities.

Have you checked you cutter.....Is you blade sharp and is it sturdy...or is it wobbling in their holder? Still didn't hear if they wavy issue is before or after sewing......

chances are your cut edges are not perfectly lined up. Take your two selvage edges and put them together -- is the fold flat or ruffly? move the selvage edges until the fold is perfectly flat. Chances are your cut edge will need some straightening. Or, you can rip your fabric to get a straight edge. I don't like ripping, because I think it stretches the fabric, but it does give you the grain line.

How wavy? Maybe it's something that will even out in the wash? Do you see wavy lines when the quilt top is all put together?

When you are sewing, watch that your edges line up with something on the machine-- a line on the throat plate or the edge of the foot. Watch that space the whole time you sew and you should have a straight seam.

I don't starch anything. And I don't press excessively. I am happy with the seams I get.

Kathy, I went through a difficult period time last year in trying to fix why my 1/4" seam was not a 1/4" seam. However I was determined ( and tearfully frustrated) and it was a combo of things. First, I had to find my 1/4" spot on the sewing machine and used 3-4 layers of blue painter's tape.
Secondly, I slowed down sewing. I was working on several log cabin squares and I had to rip out seams way back. I too have the June Taylor slot ruler but discovered it wasn't accurate. I measured every time I created a seam to make sure I wasn't 'widening or narrowing my seam allowance. Third, I had someone check my work and offer suggestions.
Fourth , I measured every time I added a log. I persevered and watched you - tube videos and bought a new 1/4 in foot with no guide. That by itself was a big help but continued to use the painter's tape. I think you need someone to assess your situation while you are sewing. I still have to careful and patient and ever so watchful ! Sometimes you just can't tell what is happening.
I hope this helps as I know exactly how you feel with this - it's a skill that takes time and care. And I am still working on it. Keep on trying and don't give up

I use steam and spray sizing if a piece of fabric is really wrinkled. Otherwise, I don't iron. I think what you are doing is pulling your fabric through the machine instead just letting it flow through (with guidance of course) Try that and see if it doesn't improve.

One more thought: Do you know how to check your fabric to make sure you have it on straight of grain? That is, fold the two ends together and putting the to selvedge edges together and allow the fabric to fall free from the edges. Are there any wrinkles showing in the fabric? If so, move one side of the fabric to the left or the right til the wrinkles disappear.
This means that the fabric is now folded on the straight of grain.