"becoming more acceptable" is a correct and usable phrase in written English.
It is typically used when discussing changes or trends in society or opinions. Here is an example sentence: "The idea of women in leadership roles is becoming more acceptable in many countries around the world."
"Here it started largely as a commercial phenomenon -- an easy and cheap way for commodities traders and banks to talk to one another -- and is gradually, as funds become available, becoming more acceptable for education communities". The booming economy and quick growth of financial companies in Russia are sustaining Internet growth here.
Some experts fear that suicide is simply becoming more acceptable.
I asked if they thought granny carts were becoming more acceptable these days; they shrugged.
Indeed, the idea of admitting one's wealth, once considered déclassé, is becoming more acceptable.
They also offer insight into how working practices have evolved recently with flexible working, for example, becoming more acceptable.
Meanwhile discounters such as Primark, for clothes, and Aldi, for groceries, are becoming more acceptable to a wider audience.
"This is becoming more and more acceptable," she said.
With time and better displays, computer surrogates are becoming more and more acceptable even for limited aspects of artwork or manuscript study, if only to select the items to be sought for examination.
Better than re-gifting, and becoming more and more acceptable, is reselling.
Using controversy in marketing campaigns is something that is becoming more and more acceptable by brands.
Maybe I was so blinded by my country's progress, visible in what was becoming more and more acceptable for women to wear, that I failed to see what was coming -- the mistakes of painting the walls before the bricks were cemented.
