What are typical reasons why leaders from other teams may have doubts or mistrust towards the data and analytics function, and what has been your approach to overcome lack of trust in the data and analytics function?

I think this depends on the overall positioning of the data analytics function within the organisation.  

There may be a mistrust due to the view that the data analytics or more specifically data governance function is there to 'police' what is done with data and therefore will be a blocker for moving forward with driving innovative use of data.  It may also be that the view is that the data analytics function is independently reporting on performance for functions and therefore also seen as a team that is a threat and adversarial.  

If, however, the function is positioned appropriately as a catalyst or enabler for the data analytics strategy and a team that can help to speed up and deliver more effectively the requirements and 'join the dots' between teams struggling with the same problems then this will significantly improve the collaboration between teams in my experience.

I’d say “being in the same frequency” with the stakeholders you are providing data-driven insights and recommendations to is most critical.

This means having a deep understanding of the relevant stakeholders business priorities and the metrics they rely on to track status / progress towards meeting their roles; then catering to these even if you disagree.

By all means still include other metrics and narrative you believe is a more valuable and reliable perspective and seek to influence those stakeholders to the extent you believe it will lead to a better outcome, but at least initially, as you are winning over the trust of a stakeholder, feed them the data and insight they already know the want and need first. Then they’ll be more receptive to angles they may have not considered/ deprioritised.

In my experience over the years and in talking with other leaders, key typical reasons are (a) other leaders/stakeholders can't get access to the data they need, (b) they feel it takes too long for the D&A function to deliver the requested data or analytics product, (c) they can't trust the data being reported and perceive it is the D&A function's job to make sure data is of high integrity.

What I've seen work best to remedy the situation is to work with the other leaders in true  partnership, prioritize on the asks, and to foster trust and credibility. This is not a once and done, fostering the relationship happens over time. It is not easy, as traditionally many stakeholders think of this as business vs. IT, or business vs D&A team. 

In the context of a prioritized specific project , it's an intentional effort to establish clear expectations with the right leaders, to communicate this consistently and (almost) at nauseam with all the relevant stakeholders of the project at hand, and to hold each other accountable -  but do this in the context of partnership and working together towards common goals. It's not an 'us vs. them', it's a let's work together to figure out what the real issue is; how we will measure progress; what success looks like/what it doesn't look like, before we even get into the more technical conversations of what is the best-fit architecture and solution to deliver for it. It takes persisting on this clarity and collaborating with clear roles, accountability, and ways of working & communicating across the cross-functional teams to build the trust and accept/work towards delivering credible results as one team. It is a win (or miss) for all. 

In short, to build that trust it takes intentional focus on building the relationships, clarity of priorities/roles/expectations, and communicating/delivering holding each other accountable.

In general, I would say I don’t find these mentioned doubts or mistrust. However, until the D&A function has a fully validated lifecycle, some doubts may appear as business users (potential D&A users) wonder about the quality of the data. It’s a matter of time that they get convinced that the data offered by the D&A service has a kind of a certification (as in PowerBI or Microstrategy).
During this period of doubt, data double-check is your best ally to ease them…

My approach to building trust has been to make sure my teams communicate with leaders from other teams, "listen" to what the leaders need and focus on responding to their need for information. That might mean building trust in data through better data quality, ensuring there is one agreed on definition for critical strategic data. 
It could also mean that leaders have easy access to information at a high- level (e.g. dashboards with some business context for correct interpretation and use, year over year comparisons etc.) which they can dig into if further deep dive is needed.