From what I've read it seems that in the middle ages in western Europe if you were lower then you drank beer and likely wouldn't drink wine unless you lived in a wine making region.

This is generally correct. Most accounts we have from the middle ages show that people preferred wine over beer when they were in a position to try both. Generally the more north you went, the less likely you would drink wine frequently unless your had some financial means.

Fast forward to today and wine is something that can be inexpensive and almost anyone can afford it. When did wine become accessible to all classes?

This would change pretty significantly in the early modern era (15th century on) particularly in France. Massive amounts of cheap bulk wine was produced for population centers such as Paris and Lyon. This increased even more so as major waterways were linked with canals and railroad systems were built. The mid 19th century was probably the peak of wine being plentiful and cheap but a series of devastating diseases hit the winegrowing vineyards and they never recovered back to that level. At least in Europe.

These days the centers of cheap bulk wine production is the central valley of California and Australia.

Also, white wine is commonly viewed as something that women drink, was there always this connotation? Or is this a more modern cultural norm/stereotype?

This mostly dates from American sensibilities in the 1970s and still probably holds true depending on the group. Serious wine hobbyists generally hold a lot of respect for white wines.