Yes, it is totally safe to show your address to other peoples.
You might need to understand three things behind your address.
1. Private key
Every address generated by bitcoin wallet, it generates a key pair: private key and public key. With some hash algorithm with your public key will get address. Anyone who owns private key means he is able to transferring your bitcoins to other peoples. Public key is very easy to be calculated by private key, so if you have private key and then you have all these three things.
2. Public key
After you transferred some bitcoins to other address, your public key is revealed with your transaction record to let other people/miner verify your signature to confirm your transaction is valid. To calculate a private key from public key is very very hard in current time, but it is possible. That's why an address is secure if it has no any out-coming transfer.
3. Address
It is easy to calculate (With hash algorithm of your public key) your address from public key, but it is impossible to get public key from an address only.
Private key --(easy)--> Public key --(easy)--> Address
Address --(impossible)--> Public key --(very very hard)--> Private key
Have a nice day.