I have been reading this thread with interest. However, this got me thinking about the evolution of the Spanish monarchy.
I only have supposition but perhaps the troubles of the monarchy, in regards to respect of the people, may go back to the early 1800's. When King Ferdinand (Fernando) VII removed the provisions of the Salic law to allow his daughter, Isabella (Isabel), to succeed to the throne. The Spanish, being Southern European, are or were more so then a male (masculine) dominated society. Therefore, per Salic law which had been effect, would have allowed Don Carlos, the King's brother, to ascend the throne.
Moreover, I Ferdinand's actions spurred off a division in Spain regarding the rightful heirs to the monarchy. I can only wonder if Don Carlos had ascended the throne perhaps some of the division caused by the ascension of his niece would have been avoided.
After all, Isabella was not a very decisive or good monarch. She had many vices, e.g., she was accused of being a nymphomaniac among others, and did not act appropriately for a person in her high position.
So, perhaps this one small act that happened in King Ferdinand's reign by suppressing the Salic law resonates today.
Maybe, at that time, the Salic law should have been observed. A later time, would have allowed a referendum, e.g., as in Denmark that allowed female succession, to permit semi-Salic law or equal primogeniture as it is now in Spain.
In summary, I'm trying to say that if the divisions caused by the event of allowing female succession by disregarding Salic law perhaps the people may respect and admire the monarchy in Spain more now. Just my opinion.
"Is King Felipe popular and beloved in Spain? Do the people look to monarchy for leadership and solidarity during times of national crisis, (e.g. covid)?"
Traditionally no member of the SRH has been specially beloved by the citizens and Felipe is no exception now. Spain was and is traditionally a no monarchical country. At a certain moment it was juancarlist, long ago, as a way of acknowledgement and appreciation of Don Juan Carlos positive role in the 23F coup.
Until a couple of decades ago, the majority of Spanish people were indifferent towards the monarchy and its members. AS long as they fulfilled their role with apparently no taint or mistakes it was nice to have them. The big festivities in the 90s (Universal Exhibition, Olympics, the Infantas' weddings) were a way to bring them closer to the people. In recent years, with the previous pact of silence from the press broken and the several financial royal scandals making the headlines, any possible or distant bond of affection has disappeared.
In this sense, and back to your question : No, the Crown does not represent any kind spiritual guide for Spaniards in times of troubles and specially not when it comes to economical crisis (in Spain, as everywhere, very intertwined with the covid crisis).
Anyway, and if you allow me, this was in my feeling not always so. I personally remember two very sad cases when the whole Spain joined together without fracture.( something very strange in our particular idiosyncrasy) and somehow felt the Crown more closer.
A) The 1997 Ermua ETA assasination brought the whole Spain to the streets (this horrendous act together with the public inconditional popular reaction against it was somehow the beginning of the end of the terrorist band.) The young Prince of Asturias presided the funeral in the Basque Country and he made a short no official speech on the spot who was very welcomed. Spain was horrified and needed to know that their King and family mourned with them.
B) The 2004 Madrid bombings brought a wave of grief and anger which left Spain completely petrified. King Juan Carlos spoke in the evening reassuring his people. Everybody was waiting to hear his words. The three royal children took part in the subsequent mass demonstration (first time any member of the RH participated in such a civic act) showing their sorrow as anyone else.
"Have the scandals of his brother-in-law/sister and father tainted him or has he been able to distance himself enough from them?
ABSOLUTELY YES. Who needs republican foes when your own family puts sticks in your wheels ? First IŮaki and wife, then Juan Carlos. Who will be next? Felipe and his team are working hard and doing apparently well. They are very scrupulous and donít go a millimeter off the script, but itís impossible - it's in human nature - not to be suspicious ( to express it mildly). A pity. I wish he can regain the trust of the people. A tough job ahead. R.