I've not heard or seen anyone state the full responsibility for the shootings is on Trump.
Humans have free will and thus are responsible for their own actions and words. The shooters in all these cases are the most to blame along with anyone who aided and abetted their crimes either online or off-line.
However, the President does set a moral and ethical tone for the country and culture and has huge amounts of influence and authority in amplifying, distributing and repeating the elements of the tone he/she wants to set. He also takes specific actions either by executive order or in coordination with his administration, the Congress and state & local authorities to reinforce that tone.
This is where Trump has exposed his true colors, beliefs and set a tone with his words and actions contrary to any American value system worth following. The tone he has set is one of demonizing the "other" and giving comfort to those who would like to act or could be persuaded to act against the "other" whoever that is for them - muslims, immigrants, free press, law enforcement, judges, people of color, women, gays, Democrats, liberals etc.
He stirs the pot, gets people riled up to serve his political ends and divide his opponents. Since his election, the number of hate crimes has increased and these mass shooting and other white supremacy/nationalism incidents have skyrocketed. That is not a coincidence IMO. Remember we are talking about 8 years under Obama and 2+ years under Trump. If we get 8 years of Trump, many more will likely die than the Obama era.
Does anyone remember that it was the Trump administration that has sought funding cuts for mental health services? Congress has rebuffed him so far, but they wanted it done. The Trump administration also was the one who repealed the regulation denying people with mental illness guns - if mental health is the driving force behind these mass shootings, why is the Trump administration taking these actions to make us all less safe?
His hypocrisy reached legendary proportions this morning with his canned statements that no one believes he sincerely means or cares about.
Attacking the free press again via tweet this morning for spreading "fake news" was laughable - he, the Republican party, the alt right media, the Russian trolls and his family spread more fake news, conspiracy theories and propaganda than anyone else combined.
Linking background checks with immigration reform was also cynicism of the highest order - gun safety and public health need to be addressed honestly and openly; no back room deals or political chip swaps should be considered for our children's lives. Despicable.