I have also some Christian friends, Hindu friends. We live together, we share everything together. But, of course with limitation. If they hold the dog, I don't. If they drink alcohol, I don't. I always try to be wise in their eyes. I told them that sometimes I possibly make mistake, insult, or look down on their religion as we have different culture and belief. I ask them, If you find me doing such, please remind me, and so do I.
Sometimes we share about what our religions teach about. There are some differences and some are the same. Alhamdulillah, we are still able to live together peacefully. I try not asking them to accept Islam or to ask them which one is right and which one is wrong. If one of us do it, I remind him/her.
As Muslim, I must invite non-Muslim. And, so do they. However, believing in a religion is not the same as joining any party whereby you can be a member just by attending their event or do what they urge you to do. In Islam, you can't. Islam comes to your heart through your understanding. Do you think all Muslims who come to Masjid or Mosque everyday and performing prayer regularly will stay in Paradise? No. If their intention is not on behalf of Allah, they do nothing. It makes sense, right?
As Muslim I must invite non-Muslim, but with wise way. No need to ask directly by asking, "Why don't you accept Islam?" It means insult them. Just tell them what Muhammad pbuh teaches us, but not all. Good teachers are they are who know and understand which lesson should be given first and when should give it. Don't do it all the time, Brothers and Sisters. Our duty is only to inform the lesson of Islam, not to make them become Muslims.
I listens to their story and explanation when they tell about history based on their religion. I give response such "As we didn't live in that era, we can't judge which one is right, but just what we believe in." We can't force others to agree with us. I try to talk more about advantages than just debating about right and wrong. My Non-Muslim friends like it, such as about how a man should respect women, should treat them in very good manner, etc.
Each of us want others to join us, to believe in what we believe in. That's normal, but must be wise. Do it wisely.