This is an excellent question, and the time to ask this question is before you cut or sew or wash or dry-clean your fabric, so you are ahead of the game!
The first thing to keep in mind is that fabrics and garments are quite complex. We think of textiles as simple commonplace things in our everyday world, but each stage of manufacture, from fiber to yarn to fabric to dyeing and finishing and garment construction contributes its own set of physical properties (and chemical properties in the case of dyeing) to the final product. In many cases, these properties are not evident to the naked eye, and they are interrelated with the properties from earlier stages of textile production. Example: even a simple 100% cotton white T shirt is a complex system: cotton fiber is an agricultural product that is harvested, cleaned and bleached and processed into fairly loose yarns (for comfort and breathability and stretch); the yarn is lubricated and knitted into a flexible stretchy fabric; the fabric is cut and sewn to maintain the stretch and comfort of a T shirt. So where does the comfort and breathability of a cotton T shirt come from? The answer is: 100% cotton T shirts are “engineered” for comfort and breathability at every stage of manufacture: from fiber to yarn to fabric to garment construction.
Below are the primary elements going into the makeup of a textile (fabric or finished garment).
Your question encompasses elements of both the fabric you buy in the store and your finished garment. I’ll start by talking about finished garments, highlighting the fabric elements relevant to your question.
Fiber Type (i.e., cotton, silk, rayon, wool, polyester, etc.).
For fabrics (not garments) this is probably the most important element you need to be concerned with. Most common fibers we wear will machine launder beautifully, e.g cotton and polyester and blends made of these.
For other fibers, for example, wool, silk, rayon, in general they can be damaged in laundering and should either receive special care (very gentle hand washing in cool water and not machine dried) or dry cleaning.
Yarn Type (fibers are made into yarns before knitting or weaving).
Yarns that are very loose can easily be damaged in laundering. They can shrink or actually fall apart. Tightly made yarns usually wash well assuming the fibers they are made from can withstand washing and drying. A good example of the “multivariate” nature of a textile is looking at fiber type and yarn type together:
Cotton knits are more prone to shrinkage than cotton wovens - not because of the cotton fiber, which is stronger when wet than when dry, but because of the looser knit construction. On the other hand, wool knits are highly susceptible to shrinkage and damage in laundering, both because the wool fiber itself is very delicate and weaker in water than when dry, and the loose knit structure will allow the delicate fibers to rub against each other and felt and shrink.
In general, woven fabrics withstand laundering better than knits because the fibers in a woven are more “fixed” in place than in a loose knit. Some nonwoven fabrics (e.g., wool felt) can actually fall apart in laundering, while others such as polyester “felt” (batting or interfacing) will maintain its shape.
Dyeing and Finishing
Fibers, yarns, fabrics, and garments are usually dyed and finished at some stage of production. In general, the earlier in the process the dyeing occurs, i.e., at the fiber stage vs. the finished garment stage, the more durable the dye will be. But this is hard for the end-use consumer to know, so always assume the worst (dye loss, dye transfer to other items, fading, streaking, etc.) Some finishes are temporary or water soluble like starch, while others are meant to be permanent if dry-cleaned - like mechanical "polished" finishes on upholstery fabric.
Embellishments and Construction Details you don't see
E.g. pearls and sequins, embroidery, fancy buttons, lace, etc., can be damaged by machine laundering. These items can often be gently hand washed but not dried in a dryer. For garments that have interfacing fabrics (stiffening in the collar or cuffs or in tailored suiting, shoulder pads, etc., these are the "unseen" elements of a garment that cannot withstand laundering and must be dry cleaned. So a 100% cotton jacket may say “dry-clean only” not because of the cotton outer fabric, but because of the construction elements you can’t see.
Some garments are “over-labeled” meaning that the item can be safely hand or machine washed even though the label states it’s dry-clean only, but going against the label is a risk if you don’t take into account all the variables that go into making fabric, and making up fabric into a garment.
Why would a manufacturer use a “dry-clean only” care label if the garment can be safely laundered? In some cases it’s a simple case of the manufacturer protecting itself from any damage claims. In others, it is because it can be more cost-effective for the manufacturer to have one label to sew into everything they make, and still in others, it may be because there is something about the finished garment that may not to be evident to you.
It is always good policy to pre-clean fabric yardage prior to construction, using the method of cleaning you plan to use after your item is made up.
Without knowing the fiber content, fabric construction, etc., of the fabric you have purchased, and the construction elements of the item you want to construct, I would follow the fabric manufacturer’s instructions for pre-cleaning your fabric. It is the safest way to go to ensure that your efforts are not wasted.
If you want to wash a fabric labeled dry-clean only prior to cutting, I suggest you buy an extra 1/4 yard and wash that before you wash your entire yardage. That way you can assess fiber damage, shrinkage, dye loss, etc., before you risk your entire fabric investment.