I would rather work with and disagree with someone who has the integrity to stand by what they believe.
I work in a group with folks of Indian decent from different religious backgrounds (Islamic, Hindu, Catholic), an Orthodox Jew, a bunch of Irish catholic types (including myself), and a person from Nigeria. We are literally from many corners of the earth, with different backgrounds, traditions, etc. If we delved into politics, we'd probably find a lot of contested ground.
Part of democracy and free society is that we need to get past those differences. If you believe that gay marriage is against your moral code, you have a right to vote your conscience. Likewise, if you campaign for LGBT rights, you have that same right, and I would make the same argument 20 years ago for people similarly mistreated for taking that stand.
I'm Catholic, and contribute regularly to a church congregation. I'm also a public officer in a secular government, whose policies are often not consistent with the church. Should I be booted out of my job (or contemplate "spending more time with my family") because I provide financial support to a religious organization whose doctrine re: things like birth control or LGBT issues are out of step with many in our society?
Where do you draw the line? Once you decide that it's not OK to think different, you end up on a steep slope.