I think you are the one who does not understand something very crucial here. First of all the word is "conscience", not "conscious".
The meaning of "conscience" has to do how
you feel about
your actions. It has nothing to do with actions of others. Unless they impose something on you.
If a Christian imposes his lifestyle/belief on others saying "you go to hell unless you believe in Jesus" is wrong. Just tell "I go to hell if I don't believe in Jesus". Don't include me.
Now the example in this OP:
Christian Baker: Making a Birthday Cake for a Trans Woman Violates My Faith
This is just pure discrimination IMO. And it is "Very Personal". The baker imposes his belief on the "trans woman". Serving her or not has nothing to do with his conscience .
A correct example of conscience would be:
1) A customer (trans, gay, straight) asks to put meat in it (red, blue whatever color) he has the right to say NO IF for example he is a vegetarian (not wanting to kill animals)
2) A customer (trans, gay, straight) asks to put an obscene picture/creation on top of the cake then he has the right to say NO [he tells this to all customers]
@9-10ths_Penguin: I hope this illustrates what I said earlier about seeing "other points" when I should be allowed to say NO (but not to trans only, no to all)