Advice you get on the Internet is worth what you pay for it. So what you should really do is talk to a local CPA. Everything I say below might be bullshit.
But, in general, you owe income taxes to the state where you live, not the state where your company is based. Two exceptions I know of are NY, which will insist on collecting non-resident income taxes from remote employees of NY companies, if their work duties do not require them to be there - it is confusingly called the "convenience of the employer" rule. The other exception is CA, which may require a remote employee to pay CA state taxes for work they do for a CA company while physically in CA. (So fully remote employees would be OK, but you might have to keep track of all the time you are present and working in CA).
However, this just covers who you owe taxes to. Smaller companies may not have the infrastructure to withhold for multiple states, and may be forced to withhold taxes for their state even though you technically don't owe that state any tax. Which may force you to pay estimated taxes direct to the state you live in throughout the year (effectively double-taxing you), but then you should be able to file a non-resident return in your companies' state to get a full refund.
My only experience with this was when I worked for a huge CA company with offices all over. They had an office in my state, so they were able to count me as a local employee there, even though I never worked in that office. They withheld the proper taxes and everything went smoothly. (Except for the fact that they never got my withholding right for my state, and withheld way too much...)