Good idea to talk about this to the therapist you have now. See what they say, since they would know what is the best thing to do in cases like this. (just read that you've already discussed this with your therapist, ok).

Well you said she did not give you a professional or home email address and that Facebook is the only way you can contact her. Probably if you just send a message to her on Facebook that's ok but the friending thing, I don't know... I did befriend a former therapist on FB and stayed on her list for many years, but deleted her in the end because I thought it is probably not good to have an ex-therapist on FB... what I would do now and what I did back then is very different, if it was now I would not add a former therapist to Facebook, back then, it would have just seemed like a natural thing to do. Have I wanted to be friends with a therapist? Yes. I will admit that. Not gonna say that I've never wanted to be friends with a T, I understand liking a therapist and wanting them to be your friend. But I am realizing more now about boundaries and professionalism thanks to my recently ex-counsellor and also my case-worker who have told me about these things. It's hard though when you really respect someone and want to talk to them or want them to be your friend, in which case, you will ask them about friendship and boundary-crossing stuff because you feel so strongly about wanting to connect with them, and then you can hear them say what is and is not appropriate, it is better to ask in real life, but i know that you have not had this opportunity.
So, maybe your therapist would add you back, maybe she would not, it's all up to personalities/personal feelings about what they want to do with the friend request. Are you gonna be really upset if she does not add you back? Will it make you sort of bitter at her? things like that need to be considered too.
There's nothing wrong with writing to her though, to update on your life, again, whether or not she wants to update you on her life, will be up to her.

Anyway I would hope a good therapist would be able to handle any political/religious posts you write on your FB and not think that you had to block them from her. But it is nice that you are thinking of her feelings, to want to block them. I'm thinking that you think a lot of this therapist since you're going to the trouble of wanting to pay $1 for it to go to her inbox and thinking of which posts are suited to her tastes.

All I can tell you is, every person reacts differently and I can't give you a clear answer on what she will or won't do because the amount of difference of opinions on professional stuff is so varying from person to person, I've had professionals who tell me all about their life, some who won't, some who hug, some who won't, some who will talk about religion, some who say they won't tell me what they think about religion, some who will give their email address, some who won't, the list goes on! I have no idea. It never is clear-cut and a one-size-fits-all, all different opinions.

Tell us how it goes anyway