MD resident working as full time employee remotely for a Delaware LLC, confusion about tax witholdings

You should see Maryland and Delaware tax withheld. You will pay Maryland state and local tax and probably Delaware tax. 

Maryland residents are taxed on income earned everywhere. Specifically, Maryland says Delaware has not entered into a reciprocal agreement with the state of Maryland: Compensation paid to a Maryland nonresident who is teleworking in Maryland is Maryland-sourced income, and therefore, subject to withholding.

Learn more at Employer withholding requirements for teleworking employees during the covid-19 emergency.

You are probably also subject to tax in Delaware. Delaware has not issued specific guidance on telework as a result of the pandemic. The general rule for the state is: 

The compensation of every person who is a non-resident of Delaware is subject to withholding to the extent that it is compensation for personal services performed in the State of Delaware, as an employee, in the conduct of business of an employer in the State of Delaware.

See Section 11: Compensation of Residents and Non-residents.

Check you pay stubs. If you are Delaware income tax withheld, then your employer considers you a Delaware employee.

If so, file a non-resident Delaware income tax return and a resident Maryland return. Maryland will give you a credit on tax paid to Delaware.

Learn more at How to I file a nonresident state return?