The Spanish Football Federation (RFEF) claimed last week that 15 of La Roja's players had pledged not to play for the side while Vilda retained his position, citing impacts on their "emotional state".
The RFEF has since offered its support to Vilda, describing the players' behaviour as "harmful".
However, Barcelona's Ballon d'Or winner Alexia Putellas, who has played 100 games for Spain, joined the rebellion by posting a statement from the disgruntled players on social media on Friday.
Hermoso was not among the initial group of 15 to write to the RFEF, but the striker – who has scored 46 international goals – has now offered her "unconditional support" for those who did.
In a statement on Twitter, Hermoso wrote: "Frankly, I wish this situation had never been made public, but I respect the decision of my colleagues, who, despite having expressed themselves privately, have been subjected to a level of exposure that they never sought.
"We all deserve respect and the space to express ourselves safely and without fear of repercussions.
"I want to start by acknowledging how privileged I am to belong to a group of colleagues who have contributed directly and indirectly to the development of women's football in Spain.
"I have always put the group first and this time will be no different because for me, defending my country is and always will be my great pride and motivation.
"Throughout these years I have witnessed significant growth and consistent evolution in the national team… which makes this whole situation that much more depressing.
"I want to publicly express my unconditional support to all my companeras who a few days ago decided to communicate the need to improve the working conditions that are experienced within the Spanish national team.
"It is important to understand that the situation we are experiencing does not happen overnight. It is the consequence of an accumulation of events, behaviours, decisions, failed attempts and mental exhaustion of trying to fight to have the players' voices heard.
"The disconnection between coach and players, federation and players and the breaking up of the group are signs that something is not working.
"I am clear on the fact players must be part of this process and that what happened a few days ago is not blackmail, nor is this happening on a whim."
Spain is due to face Sweden and the United States in friendlies next month, with Vilda expected to announce his squad for those games on Saturday.