Does this woman want to take up your offer of friendship? The fact the she has no good words for the Church may be an indication she has no desire to renew the friendship. In which case, your desire to renew the friendship is irrelevant.
It is possible to revive past friendships, but this woman is no longer the person she was when you were at school. As adults, we go different ways in life. We change and become very different people to the person we were at school. Therefore, you are not befriending the person you knew at school, you are befriending the person they are now. There are times it can be accommodated and times it cannot - depending on the extent to which both parties can accept and accommodate that change. There are people who never change but I would say they are an exception rather than the norm.
Whether anything good can come from it is something no can know. It’s possible a revival of your friendship may prompt this woman to adapt a more tolerant attitude to the Church - and it may not. You may also end up having a huge differences of opinion, causing a rift that may be difficult to heal. There’s an element of chance in any human relationship, particularly if you trying to revive a friendship for reasons I mentioned above.
I would leave the offer of friendship open, and let her decide if she wants to take it up. We can’t simply just refuse friendship to people who are not living their lives in accordance with our standard of morality. However, bonds are friendship tend to be closer among people who, among other things, share a similar point of view. If you don’t, friendship is still possible depending on the personalities of the parties involved, the extent to which they value the friendship, and the extent to which they can accommodate their contrasting points of view. If they can’t do this, the friendship will be at best strained and at worst not survive.