I found the solution in this post:
Setting up the default AspNetSqlProvider to point to remote database
So my web.config looks like:
<connectionStrings>
<add name="ApplicationServices" connectionString="DATA SOURCE=(DESCRIPTION= (ADDRESS=(PROTOCOL=TCP)(HOST=EUBEWD92Z1.jnj.com)(PORT=1521))(CONNECT_DATA=(SERVER=DEDICATED)(SERVICE_NAME=XE))); user id=user; password=pass;" providerName="Oracle.DataAccess.Client"/>
</connectionStrings>
<membership>
<providers>
<remove name="OracleMembershipProvider"/>
<add name="OracleMembershipProvider"
type="System.Web.Security.SqlMembershipProvider, System.Web, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a"
connectionStringName="ApplicationServices"
enablePasswordRetrieval="false"
enablePasswordReset="true"
requiresQuestionAndAnswer="true"
applicationName="/"
requiresUniqueEmail="false"
passwordFormat="Hashed"
maxInvalidPasswordAttempts="5"
minRequiredPasswordLength="7"
minRequiredNonalphanumericCharacters="1"
passwordAttemptWindow="10"
passwordStrengthRegularExpression=""/>
</providers>
</membership>