Conflicts and differing of opinions often occur in the workplace. Respecting the views of other people, and having them respect yours is something that needs to be worked on everyday. Whether you agree to disagree and continue with your day, the fact of the matter is that friction leads to a level of being uncomfortable. Try not to back down without having your opinion heard just for the sake of not making waves, try speaking up and voicing your ideas without trying to get anyone to agree with you right off the bat. If people are interested in your belief they will probe you for more information and will be able to come up with their own ideas on the suggestion.