And thus the tyranny of the majority.

The perils of democracy. The "tyranny of the majority" is a fundamental, ineluctable aspect of democratic systems. The majority gets to decide what the rules are and can impose those rules on the minority. Those rules are based on what the majority conceives of as the Good. Democracy isn't a mechanism for finding the right answer to problems; it's a way of making decisions when everyone doesn't merely disagree on what is good, but when people are different as to what society would be good for them.

And render unto Caesar what is Caesar's -don't shove your morality down our throats.

They would argue that there's no avoiding it. That you shove your morality down their throats all the time.

Many people - and I think many non-religious people - conceive of religion as a matter of individual liberty, of individual faith. That religion is mostly a matter of personal conscience. Which is certainly how some religious faiths operate.

But not all of them. For example, Judaism isn't really something that is purely internal to a person. To be Jewish, you have to act Jewish in the world. You have to be part of a Jewish community, follow Jewish rules in your dealings in business and public life and in interacting with non-Jewish people, etc. That's why there's no monastic or hermit tradition in traditional Judaism. Being Jewish isn't a thing you believe in the privacy of your own home or in your synagogue- it's a thing that you and everyone in the Jewish community does and does together, all the time and in all places.

Your conception of religion - that faith is something that people decide for themselves and don't/shouldn't tell other people what to believe - incorporates certain beliefs about religion and morality that are not universal and indeed are highly contested. It's part of why religious advocates tend to get upset at the idea that there even exists a secular state, because what modern liberals (small "l") conceive of as the secular state is itself an idea about what "religion" is, and is therefore a religious statement. It's an analog to the criticism of supposedly "neutral" institutions like courts or the media, where radical critics will argue that there's actually no such thing as an unbiased court or newspaper - the court or newspaper always has a set of biases, it just proclaims them to be so universal that they are beyond dispute.