CDI is not yet a well-defined category and is used in various contexts today. However, tracking is a core component of Customer Data Infrastructure and therefore, it makes sense to categorize purpose-built tracking tools as CDI. If you have better ideas, I’m all ears!
It’s helpful to keep in mind that all the CDI solutions mentioned here are, one way or the other, alternatives to Segment Connections. But unlike Connections, these tools don’t ingest data from secondary or external data sources.
So, in alphabetical order, here are various CDI solutions worth exploring:
Avo enables you to create a smart tracking plan using an easy-to-use interface and then generates code for your developers to implement tracking based on the events and properties defined. This gives product managers more control over the taxonomy and eliminates the scope for errors during implementation.
Freshpaint offers a hybrid solution wherein besides tracking data via code (which is always recommended), you can set up auto-tracking that gathers data without code (also known as implicit tracking). The hybrid approach brings more flexibility to teams with limited engineering resources. 
Iteratively is an alternative to Avo and they both have a similar approach to tracking. They both offer limited integrations but integrate with Segment as a destination, allowing you to further send data to all the destinations supported by Segment.
This might seem odd as Iteratively and Avo are also alternatives to Segment Connections but it makes sense to use them in conjunction with Connections until they expand their destinations library.
MetaRouter is a relatively new solution that is focused on server-side tracking and offers private cloud and on-premise installations which are ideal for larger companies with stricter norms for data privacy, security and compliance. 
Rudderstack also offers multiple products but their core product is exactly like Segment Connections. However, besides offering a cloud version, RudderStack is open-source allowing you to deploy it on your own servers if you have the resources to maintain an open-source product.
Snowplow calls itself a behavioural data collection platform that is also open source and also offers a cloud version. Snowplow’s approach is different in that it only syncs data to data warehouses and doesn’t support any other cloud destinations.
Also, implementing Snowplow requires expertise in its proprietary technology and is therefore only suitable if your company has a dedicated data team.