Can a judge remove full access to my children because I am transgendered?

Quite frankly, transgender parents used to be consistently and frequently discriminated against because they were transgender.  Even though some judges are still very conservative, the issue is not as much of a custody "death nail" that it used to be because of the increase in awareness.  That is not to say that it won't have an impact, though.

The stardard for determining custody is the best interest of the child.  In order for the court to deprive you of access to your child, they will have to have more than just the argument that you are transgender.  There must be some evidence that you are a danger or harm to your child.  For more liberal judges, the fact that you are transgender will not be a problem.  For more conservative judges, you need to be prepared to show that your lifestyle will have no effect on your children.  The judge may also place restrictions that include no adult individuals can reside overnight during periods of visitation (much like they do with boyfriends and girlfriend clauses.) 

You may or may not be able to get it stricken from trial.  In order for it to be admissible, the other side would have to show that it is somehow relevant.  If you can focus on your positive traits as a parent, your attorney may be able to keep the information out.  If your ex- can show that your choices have somehow harmed the child, then yes it will be used as leverage against you. 

Even though it's stressful that there is still this type of discrimination, you focus should still be on the best interest of your child and demonstrating that you are a good parent for the child.  During trial or any other hearing, present ample evidence about your good parenting traits.  This is called making a good record.  If you do have a judge that is biased, a good record will help reverse the discriminatory effects of the judge's emotions.