Marvel is currently one of the most popular franchises in terms of movies and comic books but it has been involved in some controversy for a few reasons.
X-Men movies had to be completely ignored when the MCU made its debut in 2008. However, things got netter when Disney acquired the film rights.
The elements of Queerness were not liked by the fans for being included in The Young Avengers. Things took a worse turn when Young Avengers was relaunched in 2012 and it received a negative response.
Mystique was also a member of the Brotherhood of Evil Mutants. The entire team later worked for the US government and they got the jobs because of Mystique’s black ops credentials despite that they tried to assassinate a US senator.
Marvel sold the film rights of Fantastic Four to FF and they were marginalized by the publisher. But they could not succeed much and Marvel canceled the book for a long time until Disney acquired the film rights.
Marvel once tried to make Inhumans equivalent to the X-Men. However, they slowly started to bring the Inhumans in opposition with the X-Men making their Terrigen Mists harmful for mutants.
Following Avengers Vs. X-Men, the Avengers Unity Squad was formed and they were just some mutants going against Scarlet Witch. Inhumans also joined the team.
Cyclops and Wolverine had to go through a lot when their relationship to the X-Force was disclosed. They did terrible things but were always considered important.
Although the Ultimates were the Ultimate version of the Avengers, the inclusion of violence and juvenile humor made them controversial.
The New Warriors tried to introduce a non-mutant teen team but the response was mixed. Although Safespace and Screentime were introduced, it was criticized by anti-SJW m embers and all those who believed in diversity.
The Illuminati was formed to stop threats but while they went to do that, things always took a worse turn. This made them a kind of villain for the franchise.