They are to be celibate or potentially be "disciplined" (disfellowshipped or worse.) Technically this doesn't mean ostracized. But in reality, it often is in practice ostracization.
No they are not b/c they are gay ppl all over.. there are gays and lesbians in every Church. No, they are not otracized they are simply wrong.. like any other sin.
Anyone is allowed to stay in church unless they are being disruptive.
You can be gay and be a fully participating Mormon, however, you can't act on it. Being gay is not what is considered a sin. Acting on it is.
You also cant actively go against the church on the issue and then expect to be able to hold any callings and sometimes it can lead to you be excommunicated.
The reason is because the members of the church are the ones that hold all the callings and make the church run. They wont let a person that is actively trying to go against the doctrines of the church be in a calling or hold a position in the church.
You also make covenants at baptism to uphold the standards and beliefs of God and if you are actively working against those covenants, then they no longer apply to you and the church won't keep you listed as a member in good standing.
Excommunicated members can still go to church, however.
Yes, they are allowed to stay in the church. The church separates the behavior from the desires of the individual. They aren't judged for having desires for the same sex, but they are expected not to act on them, ie to remain celibate just like anyone who cannot marry in this life is expected to remain celibate.
If they remain celibate, then they can be full members as far as a single member can be. That includes going to the temple, holding the priesthood (for men) and everything that entails. While they may not be able to be something like a Bishop (since that sort of requires being married) there's no limit so long as they are not sinning sexually.
If they mess up and sin, but are repentant and continue to recognize the behavior as wrong and try to be celibate, they can be forgiven and go through repentance process. Sexual sin typically takes a full year of repentance, including celibacy/abstaining from the sin, and depending on how often it's happened and the severity of the sin they may be excommunicated in order to remove the priesthood and higher covenants and start them on square one again, making repentance easier. We believe that when you make promises to God you are more accountable, so sometimes when someone has sinned it's much harder for them to come back to God unless those promises are wiped clean so they can start from the ground up again.
If they are not repentant and see the behavior as perfectly fine, they may be excommunicated and disfellowshipped. This basically means that they will have their church membership removed (since the church teaches that homosexual behavior is wrong, they would be going against church beliefs, so it's sort of natural.) They would still be allowed to go to church, they would probably be asked not to take the sacrament but I've never seen someone refused who wanted to take it, and contact with family would continue of course, temple attendance would not be allowed, and they wouldn't be allowed to pay tithing, bless the sacrament (men) or do any priesthood things (men.)
Considering I have a gay sister who the family has never been counseled to cut off contact with, and a gay friend who's brother and family are members and they treat him and his partner with great love and as far as I know have never been told to cut off contact, and I have never heard the church ever say to cut off contact, that is an individual choice that people make, not one that the church advises.
Add: I have also had several family members excommunicated. Some continued to go to church, repented, and were rebaptized. Most just left the church and never went back, they had basically left the church before being excommunicated (they do it to your face unless you aren't around, that's the only time they'd do it by letter, and usually they would ask you to come to a disciplinary hearing and when you don't show then excommunicate and send the letter telling you the outcome. It's never just a letter.)
Never once has people ostracized those in my family who were excommunicated since that was kept PRIVATE. The only way you know someone has had a disciplinary hearing is if they tell you, and the only way you know someone was excommunicated is if it involved you or they told you. If someone else tells you, they can be in big trouble. The only time ostracization seemed to happen was when they were doing things that would naturally keep members of the church away or moving into circles away from the church, they kept their friendships from before without issue. I mean, we don't drink, so when my sister was going to bars those friends of hers in the church naturally stopped hanging around her. Not that strange... though they still ask about her and how she's doing and seem concerned about her welfare, and I never hear them speak badly about her. It has far more to do with people not wanting to be around the behavior they are doing than anything going on at the church.
Does this mean that some gays would be ostracized? Sure. Especially if there are younger children in the house and the person is very in your face about their sexuality, the parents may decide to limit contact or ask for strict rules (like one of my mom's friends insists her son and his partner stay in separate rooms when they visit for the holidays.) But most families don't ostracize anymore. It DID happen a lot in the past, and that's why they don't counsel doing that. It's just not loving.
If you want real church experiences, check out the book "No More Goodbyes; Circling the Wagons around our gay loved ones" by Carol Lynn Pearson. Her point of view is pro-gay-marriage, but the book talks about many different experiences of gay people in the church, and how their families reacted. Some were ostracized. Many many weren't. And these days, I don't know anyone would would cut off their gay family or friends unless there were strong reasons for it. The link I gave directly counsels against making the gay person feel like they aren't part of the family anymore.
No. They will be excommunicated by a formal letter. I saw it happen to this Australian lesbian in a documentary about her returning to Utah to meet other excommunicated people...not all were gay or lesbian excomms I might add.
The woman's Mormon family were also forbidden from contacting or associating with the excommunicated person again, despite one of them being the woman's own mother.