LGBTQ+ and labour laws are very different across countries, so it's very difficult to talk generally about how this works without being specific to some country.
I will talk about Spain because there's where I am from and where I worked most of the time.
You generally just cannot fire someone for arbitrary reasons before their contract comes to an end. You really have to justify why you need to fire that person, like having several poor performance reviews against them. Otherwise, you may risk having your firing judged as "unjustified" and having to pay that person a big compensation or even the firing being judged as void and having to readmit them to the position you fired them from.
No matter whether they are cis, gay, straight, man, woman, POC or whatever, you just cannot fire someone without a valid reason unless their contract has come to an end and you don't renew it, that's basically it.
So could someone argue that your sexual orientation or gender identity is a valid reason to fire you because being gay doesn't fit within their company culture or having trans people may cause them an image problem?
No, article 4.2.c of the Worker's Statute says you cannot be discrimanted for employment based on sexual orientation or gender identity, among other criteria like ethnicity, age, union membership, etc.
So you couldn't be fired for being either gay or straight, man or woman, cis or trans, etc. Nothing of that is a valid reason to be fired.