"Pushing" in the context of giving opinions or views carries a context of trying to persuade in a forceful way. For example a person may be described as "pushy" if they are excessively assertive.

Someone described as "pushing their opinions upon others" means they are trying to persuade others to take on the same opinions, or perhaps trying to present their opinion as the only valid one.

"Pushing" in the context of giving opinions or views carries a context of trying to persuade others in a forceful way. A person may be described as "pushy" if they are excessively assertive about any subject.

Someone described as "pushing their opinions upon others" means they are trying to persuade others to take on the same opinions, or perhaps trying to present their opinion as the only valid one.

eg.

"Please stop pushing your views about veganism on me."

It is somewhat different to the term "peddling", an old-fashioned word for "selling" that has come to be a pejorative term describing someone who spreads their views or ideas:

eg.

"A former Alaska lawmaker has pleaded guilty to a state count of letting unregistered lobbyists peddle their ideas to him."

"Peddling" carries the idea of spreading views to as wide an audience as possible, whereas "pushing upon" more suggests trying to persuade a specific, possibly captive audience.