Yes, but why do they file that way?  It usually end up costing more taxwise.  Are they in a Community Property State?

they file separately because my son in law has a business and he always has to pay in.  my daughter claims the kids on her taxes per their agreement prior to being married but now they bought a house in 2020 and she wasn't sure if they could still file separately or not

They have children?   And they are filing separate returns?  Do they understand that they may be losing child-related credits by filing that way?  

To answer your question about buying a house---they can file jointly or separately--as they please.   If they file separately again they can divide up the mortgage interest and property tax between them if they want, so long as the total entered does not exceed 100% of the amounts paid.

If you were legally married at the end of 2020 your filing choices are married filing jointly or married filing separately.

Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $24,800 (+$1300 for each spouse 65 or older)  You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit. 

If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI)

 If  you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states

https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separ...

They can still file separately ("Married, Filing Separately") - owning a house together does not affect their filing status options. 

One of the main requirements for "Married, Filing Separately" is that both spouses must use the  same method for calculating deductions  - standard or itemized.

If they choose to itemize deductions, they can allocate the deductible mortgage interest and property taxes in any way they wish.

@xmasbaby (above) provides excellent additional detail on the limitations, advantages and disadvantages of "Married, Filing Separately"