The RSAKeyValue, Modulus, and Exponent tags are in there because you used the method ToXmlString().
An RSA public key is made up of the modulus and the public exponent. There is no security issue with distributing these 2 items. HOWEVER, you do NOT want to distribute any of the other items in the Private Key. The private key has these fields:
<RSAKeyValue>
<Modulus>…</Modulus>
<Exponent>…</Exponent>
<P>…</P>
<Q>…</Q>
<DP>…</DP>
<DQ>…</DQ>
<InverseQ>…</InverseQ>
<D>…</D>
</RSAKeyValue>
Do not distribute anything other than the Modulus and Public Exponent, which are found in both the Private and Public key.
When public keys are distributed, they are usually done by giving out a signed X509 certificate, which contains the public key, identification information linking that key to an entity, and a signature from a trusted authority.
If you give out the public key in the XML String format, the receiver must then use the FromXmlString() method to use it. The receiver also has no way to know if it is you who really sent the public key unless you give it to them in person (or use the certificate method above).