Once you know what you believe and why you believe it, you must live it out. Beliefs must never be just an academic exercise. If they are what you truly believe they should influence your whole life, not just part of it. For people of faith what we profess on our days of worship must be what we live out the rest of our days. The pew must meet the pavement.
Involvement by people of faith in government does not mean using the power of government to coerce common beliefs, for belief can only be shared, not dictated. It is a matter of the heart. But faith should influence how,why,and what we decide in every part of our lives and that is true in the large context of society as well as in our own homes. If government is truly "we the people" then it should be an expression of the faith of "we the people".
This crosses the lines of faith traditions. To take one example - the treatment of the poor is a key to three main religions. For the Jewish the practice of gleaning (Leviticus 19:9-10,23:22,Deut.14:28-29) is part of the Mosaic Law as well as "love your neighbor as yourself"(Leviticus 19:18). The New Testament talks about "true religion before God" as including taking care of the widows and orphans (James 1:26-27). Most of the time people focus on doctrinal purity, but forget that first of all God cares about people and their welfare (ref Matthew 25).
And it is good to remember in these troubled days that alms giving -charitable giving to the poor - is one of the Five Pillars of Islam (interestingly the Arabic word for alms - Zakah - is similar to the Hebrew term for charity -Tzedakah) Too often nowadays Islamic charities have been viewed with scepticism, but it is an essential element of the faith regardless of those who misuse it.
How can you work to ensure that the beliefs you espouse are your own? First after examining what you believe and why you believe it, don't be afraid to share them. Try being the first to answer in a group when questions are asked. Sometimes if you always wait to hear what others say first there is a tendency to play it safe and be a "me-too" ,especially if your true views diverge from what seems to be the group view. Listening to others is important ,and just being "contrary" isn't courageous, but be true to yourself and don't just adopt a view that you don't believe in just to avoid "sticking out".
Write down or record audio of your thoughts and views, then read or listen to them again and see if they make sense or sound in any way "false" or "pretend". It is good to be able to listen to yourself and detect when you are not being real.
Walk in others' shoes - try to imagine how others would hear you,how they would view the things you do and maybe see them a different way,with a different perspective. Imaging yourself living somewhere way different from where you are and see how you would view the world.
Finally, focus on being known for what you are for, not for what you are against. There is a time and place to criticize and call others out for wrongdoing, for sure, but too many people are only known for the things they fight against and not for what they support. Aim to build, not destroy.