I found a way to use both CDI and a custom jackson configuration. The trick is to exclude the configuration from weld in beans.xml:
<?xml version="1.0" encoding="UTF-8"?>
<beans xmlns="http://java.sun.com/xml/ns/javaee" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xmlns:weld="http://jboss.org/schema/weld/beans"
xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://docs.jboss.org/cdi/beans_1_0.xsd
http://jboss.org/schema/weld/beans http://jboss.org/schema/weld/beans_1_1.xsd">
<weld:scan>
<weld:exclude name="your.custom.JacksonConfigurator" />
</weld:scan>
</beans>
In case your jackson configuration is not recognized, add the following context parameter to your web.xml
<context-param>
<param-name>resteasy.providers</param-name>
<param-value>your.custom.JacksonConfigurator</param-value>
</context-param>