You can have these thoughts Haley. You can question yourself on WHY you believe a certain way. That's your personal issue to deal with. Whether or not you are able to not let it affect your "Professional" abilities as a leader or follower, is totally YOUR CROSS that you must bare.
You can be as introspective as you want. While I have a number of college degrees, my first (AND FAVORITE) was my degree in Psychology. Especially looking into WHY people act the way they do. Much of which bled over to Sociology. Most people act a certain way because they are a product of their environment. But non of that really matters. Wanting to be introspective and asking yourself WHY you feel a certain way is great. It may even help you to become a more well rounded and knowledgeable person. But it isn't germane to being a good leader; or follower. Well..... I will qualify that and say that nothing is ABSOLUTE. I am sure there are some people that aren't able to keep their personal beliefs out of their professional life; but again, that's a personal issue that the individual has to deal with.
In the military, there are plenty of rules, regulations, and decisions that are made everyday that I didn't agree with; yet, I was able to support, follow, and lead others in those policies. I was able to separate my personal feelings. What if I'm a conservative republican and you are a liberal democrat? I can still treat you fairly and be an objective leader. What if I'm a christian and a person who works for me is a satan workshipper. I can still lead in a professional manner and be fair. It is ok to disagree with another person's beliefs, lifestyle, or a range of other things. You can still be fair and professional with them.
Now...... if you CAN'T...... then you ARE DISCRIMINATING. That is NOT acceptable. But don't think that it's not possible to be able to differ with a person and not be fair and objective. That's the problem with a LOT of society and the PC culture. That is why DADT (Don't ask - Don't tell) was such a BAD THING. It promoted the ostrich syndrome. (Burying your head in the sand). "If we don't talk about it, it doesn't exist". Like not talking to your son/daughter about sex or drugs, and being shocked if one is/gets someone pregnant or is using drugs. You can be as introspective as you want, and try to figure out why you don't like a certain thing. So what if you FIND THE ANSWER. What if you still don't want to change your position?
If you STILL don't want to date someone of the same gender, or believe it's right, should you have to quit the military or quit society? What if I still don't want to date a girl who weighs more than 120 pounds. What if I still don't want to socialize with liberal democrats? What if i still don't want to marry a person of a different race, color, or nationality? The same can be said in the opposite. If a person is gay, as a leader, isn't it possible that they may not be able to be fair and professional with the heterosexual? Maybe the liberal democrat can't be professional and objective with a conservative republican that they supervise.
It is good to be introspective. Most people do it everyday about something, and don't even realize it. It is what helps you grow. It's what helps you mature and evolve in your life. But the WHY you believe the way you do, is NOT IMPORTANT. What IS important, is HOW you BEHAVE. That is the indicator on whether you are able to conform to society. And that society could be the military, the company you work for, the friend/acquaintances you associate with, the social laws you obey, etc. This is what is important. This is what makes a society work or fail. Not why people believe as they do; but how they behave. Behavior is where RESPECT comes from. Yes, some BEHAVE out of fear of discipline, incarceration, etc. But MOST people behave out of respect. "Live and let Live". I have friends I totally disagree with over many social/religious/political issues. Doesn't mean I can't still be friends with them. And I've lead a lot of individuals, and have BEEN LEAD by a number of individuals, where we didn't agree on a lot of things. But we knew we had a job to do, and we were able to move on in a professional manner.
So, if you need to LEARN WHY you believe as you do; in order to make you an objective, fair, and professional leader/employee; then that's fine. That's how you found to work out your issues. But that's not necessary for everyone. Some people can simply accept that there are things around them that they don't like, agree with, etc. but they know that they have to accept them in order to fit in and be part of that society.
On a personal note: I LOVE diversity. It's what makes life interesting. I DON'T WANT everyone to think the same way. It's ok for people to have different political, social, religious, perspectives. I have no problem with those who think differently that me. What I want however, is respect on both sides. Both sides can be discussed, debated, and even argued. And hopefully each side will learn something. Maybe their beliefs become stronger. Maybe their understanding of others is improved. It is healthy. I don't want everyone to believe that a gay lifestyle is good. I don't want everyone to believe that conservative values are best. I don't want everyone to think only 1 religion is the right one. I want the differences of opinions. But I want each side to respect the other side. (Unlike protesters who say they are exercising their right to FREE SPEECH, but in their protest, they STOP the other side from exercising their right to free speech). That is discrimination. That is wrong. Differences are good. I don't care so much of WHY you believe as you do; as I do on HOW you behave around those you disagree with. The WHY part is the INTERESTING part. The HOW is the IMPORTANT part.