Many wards and stakes hold social events outside of the regular Sunday meetings, like Christmas dinners or an evening of musical performances. These activities are a great opportunity to introduce people to the church community in a more casual setting. When you go to activities, keep an eye out for people you don’t recognize and introduce yourself.
The next time your ward or branch cleans up the community or helps a neighbor in need, extend an invitation to friends. The Church has great working relationships with many humanitarian organizations like the Red Cross and Catholic Charities. Are there organizations in your area you can partner with like a local food bank or a school? Service can open hearts and change the perceptions. It blesses both the person being served and people who serve them together.
If your elders quorum holds a chili cook-off, invite friends to compete. Get the word out on social media that anyone is welcome. Consider cooking a few pots for the local homeless shelter or delivering leftovers to someone who is ill. If the Relief Society holds a Christmas party, who else can you invite? Is there a charitable cause you can theme the party around like Sub for Santa or making refugee kits? Treat your events as neighborhood gatherings rather than Church activities.