Is "Made in ___" a factor when you buy clothes?

One cannot generalize -- it depends!

China for silk apparel and accessories ( they discovered how to make silk!) -- they generally do not need drycleaning. Japan also has exquisite high-fashion taste but cost of production there is likely influenced by high wage levels, so one does not see much fashion stuff outside of the country (unless it is high-end or luxe)

A lot of labels now indicate where it is designed and where it is made. If you buy some clothes in Paris, you will see that they could either be manufactured in France or outside France.  Sometimes the production source is indicative of where the best materials come from (such as shoes designed in Paris but made in Italy). One amusing thing is the making of perfumes which come from natural materials -- ingredients may come from different parts of the world ( depending on where they grow or are sourced best -- could be Africa or Asia or wherever) but the technology and the " nose" may only be available in a country like France.  Also, in some cases where a franchise operations has the clothes made in the local country, it is sometimes indicated that the raw materials come from the country which owned the franchise.

Also, it used to be that place of production is indicative of longterm durability but in present-day culture it is more of a throwaway culture. In general, we tend to discard stuff fast in favor of new fashion. Zara has such a company philosophy -- they make clothes ( maybe in Asia or northern Africa or elsewhere) but the fashion is replaced after a very short time.

Some countries could have excellent fashion and accessories and still relatively cheaper ( such as Spain) but eventually that changes and the price levels seek how other more expensive countries price their goods.